Gate's Lab looks stupid when viewed on YouTube out of context. What nobody seems to realize is that air-dashing is a standard feature in X6 (why you UNCONDITIONALLY start with the Falcon Armor, unlike X5 where unarmored X is your punishment for picking Zero in the intro). The game is designed accordingly, and as awesome as Shadow Armor is, the difficulty with which you have to obtain its parts should probably cue you in to the fact that lacking an air-dash requires some manner of compensation. I admit it's a departure for the series that can take one off-guard pretty easily, but after either 8 levels or High Max, you REALLY ought to have figured out that your equipment matters (especially since Yammark's hidden pit is a LOT worse than Gate's).
And at least you CAN compensate for this in some way. In X5, if you pick Gaia Armor in the first Zero Virus level (which is realistically the first "new" level in which you have access to it), then you are [tornado fang]'d. What everyone bitches about in X6 is not its end result, but rather its learning curve and lack of direction. Not saying everyone has to like it, but seriously, stuff like that passed in the 80's without comment. Had X6 come out in an era where player's guides were an expected part of the culture, this would be a non-issue (and we all know Classic NES games did this, what with such tomfoolery as the Magnet Beam and the ever-cursed Crash Bomb ammo).
Okay, never really was bored enough to read all of this post, and I most certainly don't expect to change Soultrigger's mind as I do acknowledge that X6 isn't for everyone. But, a niche audience and a poor quality are not the same thing, so here we go:
In terms of "visibly intentional", I would only say these are: X (Ice Burst+Jumper), Shadow Armor, Zero (Hyoroga). That's only 3. I don't think Capcom had Blade Armor with Ice Burst in mind as very few people are even aware of it. I definitely don't think Capcom had in mind using invincibility, reducing descent speed, or even very tight double jumps as viable options (and if they did, they're idiots for expecting the players to come up with or even execute these).

(Yes, "that image" is back. Blame the AA news)
Why, then, are the wolves at every ledge, coupled with the fact that the first jump is easier than the rest? That enemy placement is as obvious as the Bat Bones in X2 (in Serge's stage, damage barrier use is required if you skipped the capsules; something the game designers clearly intended as a viable option since it alters the ending slightly). And I REALLY should not have to tell you how often X6 uses that same "barrier abuse to block spikes" trick; it's particularly well known in Wolfang's and Turtloid's levels.
"Jumps are too tight to be intended" is not a viable argument against Zero's double jump. By that logic we've been cheating at an awful lot of Rush-required areas in the Classic series (Snake Man and Magma Man both come to mind)
The only thing I will grant as POSSIBLY unintended is the descent speed from special weapon abuse (not applicable to the spike wall, but still). And even that is arguable; there are a lot of obstacles in the game that are built with the expectation that the player knows how to squeeze the most out of the game's physics (ie: Metal Shark Player's hidden path). However, it is a tactic that I personally consider cumbersome and useless; it is outweighed by Hyper Dash in every conceivable situation, and I've only toyed with it for the sake of argument/research. The fact that the second Mega Man game to ever have timed leaderboards redid pause screen mechanics also suggests that this is not intended, as does the fact that Speedster, otherwise a useless part in X6, can be permanently lost.
The thing is, it's not THAT difficult to program an obstacle that is destroyed by a specific weapon. Not only does the rest of the series do it, and not only does X5 do it in some extremely ill-thought-out applications (LET'S REQUIRE THE SAME WEAPON YOU GET IN THIS STAGE!), but they actually do this in X6 with the Nightmare System obstacles. If they wanted to require one arbitrary solution, they'd have done so.
The problem I have with these visibly intentional solutions is that, for X, requiring Jumper (which is simply a Part) or Shadow Armor is excessive for the player. They're inconsistent with the design philosophies of the prior games, from which X6 borrows from. If X6 intended to deviate from those philosophies, the requirement element should have been more frequent throughout the game (either before or even after), rather than dropping the news to the player suddenly that X6 decided to do a 180 on imposing an upgrade search requirement, and then completely forgetting about it after that specific part of the game (Gate Lab 2 seems more like a design oversight than an actual "requirement", because it takes Falcon as base but completely forgets about Shadow). Or, at the least, they should've made Jumper easier to obtain and/or a lot more prominent than the other universal green Parts. A firsttime player may not even know of its existence: if such a part is so important, why does the game give such little attention to it?
I don't think anyone would argue that X6 isn't something of an odd-ball to the series in that regard, whether they like it or not is another question. So, yes, it's inconsistent, but it's not without warning. The alternate routes in the game actually DO telegraph this concept, most notably Metal Shark Player and Rainy Turtloid. The "main" levels are not viable because the philosophy of the Stage Select screen means that any one of them could be your first level (and as we're all well aware, Heatnix takes enough flak for this as it is; those minibosses are pretty easily dismantled with proper equipment but are a royal pain with only default gear).
I acknowledge that this roadblock is meant to force a firsttime player to go back and collect power ups until they have enough in their arsenal so as to be prepared for the endgame. However, in that regard, I feel that having the option of beating High Max to skip to Gate Lab is contradictory to it: why bother giving the option to skip to the final stages if you're just going to force the players back to the original eight on a search quest?
High Max himself IS a roadblock because he's unbeatable without an appropriate special weapon. It's not a literal check point, of course, but it's an obvious red flag of the design philosophy. Coupled with the early spike wall and the frequent difficult jumps in the alternate paths, yeah, I'd think twice. Or at the very least I'd accept the consequences of my own rash curiosity as being my own fault.
I also feel that, as a "mental challenge", it doesn't belong in a game like Mega Man X as a roadblock obstructing the path to completing the game (in other words, this type of challenge is better suited for an out-of-reach upgrade/collectible).
It's not as if that mentality can't be taken to its own extreme, though. X5 is a textbook example of such as it creates a very overly linear game compared to the rest of the X-series.
As a challenge, it is not very approachable, and thus turns off a lot of players who could've potentially (although probably unlikely) enjoyed the rest of the game. It is also not balanced: why does Zero only need Hyoroga while X (Falcon included) needs its equivalent AND Jumper?
Probably because Zero requires an extra part to not get ripped apart at twice the rate X does. From the standpoint of "offense, defense, mobility", the balance is pretty obvious: Falcon is the all-rounder, Blade trades offense for mobility, Shadow does the opposite, and Zero trades defense (and range) for mobility and power.
While X5 did have some irreversible events that had negative consequences for the players, neither X4 nor X5 mandated that the player had to start over from the stage select.
Outright impossible, perhaps not, but on the topic of "tight timing", the previously mentioned Gaia in ZV1 trounces any difficult-to-time jumps that X6 ever presents, and that DOES require a trip to Stage Select to rectify.
What is the point of lives?
Same reason they exist in any other game: In case an enemy kills you or you die due to player error. And in X6, the general "standard" of both enemy power and enemy numbers is much higher than normal (granted, I play on Xtreme mode all the time, but I do the same for X5 and there really is no comparison). It actually balances quite well with the fact that X6 removes all of X5's asinine power-up restrictions, thus allowing for much stronger and more customized characters with more or less the same pieces of the puzzle. But it makes starting out even more troublesome than the usual as well. It also couples with the Reploid rescue system amounting to 16 one-time extra lives: You get a "crutch" for your first time exploring a level. For revisits, you need to step it up.
As for "Continuing" at the exact same spot. ...I got nothing. But I'm pretty darn sure that X6 is not the first Mega Man game to do that. And to this day I still play a lot of games where I kill myself deliberately because it's the only way to restock your lives if they fall below the default, so...yeah. Common problem with the industry.
To be clear, at no point would I call X6 "approachable". It isn't. But not every game is supposed to be (again, I call it "Mega Man X: The Lost Levels" for a reason). That factors into challenge, and to me, challenge has little relation to quality. There are hard games that I enjoy and easy games that I enjoy just as much. What constitutes a "fair" challenge is an eternal debate that I have no expectation of settling here (I believe the Zero/ZX concept of "Hard Mode" to be conceptually and thematically worse than anything in X6, but hey, that's me).
X6 was a title that suffered in quality due to being rushed. "Suetsugu stated that the development schedule of Mega Man X6 was tight." If even the artist admits the game was rushed, I don't see why people can't accept the fact that many aspects of X6 was not actually intentional/well-designed and that, had the developers been given more time to polish and QA them, they would've definitely changed.
First of all, nobody who's seen the boss sprites or the localization will debate that. Second, I've acknowledged the lack of an unconditional "exit" button and the fact that Sentsuizan's controls are inexcusable, right? X6 is not trying to be Metroid; it takes steps in that direction, yes, but Mega Man has yet to do the "open world" thing on anywhere near that level of quality, and I don't believe that's what X6 was trying to do. The existence of the Stage Select screen is not only clearly intended but is accommodated to a much better degree than X5 did. For how tight X6's production was, its level design and power-up accessibility was ultimately better thought out than X5's, which took longer than normal in production. That, I believe, speaks volumes. The so-called "grand finale that Inafune intended" is one of the most overall restrictive layouts that the series has ever seen, and is the eternal reminder to me that time =/= quality.
We all know that X6 has its rough spots, but it has better "bones" to it than most, and the unique balance between difficulty and power-ups creates an equally unique appeal and gratification when compared to other X-series entries.