I don't think they "accidentally" built a spike wall that has 7 different clear methods, including some EXTREMELY convenient enemy placement for barrier abuse (something X2 did on a smaller scale, BTW). And that's where most of the bitching comes from.
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).
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 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? 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). 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?
A much better example of this kind of design is in Super Metroid. A firsttime player does not know about advance techniques like wall jumping or infinite bomb jumping, and assumes that in order to get Spazer Beam, one must skip ahead to the next area, only to later return once they have found the necessary requirement to get it. In doing so, they must enter Norfair, obtain the Hi-Jump Boots, then backtrack to said location. However, a clever player, even on his or her first playthrough, may realized that one can reach infinite height through bomb jumping, and thus circumvents the height requirement needed to get Spazer Beam. This grants a power upgrade earlier than intended, making the game easier and faster. On the other hand, an experienced player who has been exposed to and mastered walljumping can simply, quickly jump up. In this sense, the game is both approachable because it allows new players to find the easy solution but also deep/clever in that it rewards players for coming up with or knowing beforehand a better, more efficient solution.
Besides Zero, X6 does not have an approachable method (unlike Hi-Jump Boots, Jumper and Shadow Armor aren't exactly easy to get for firsttime players). X6 merely has different methods, and in X's cases, all of these solutions can be considered too demanding, in the sense that it is unprecedented for an X game to require miss-able upgrades to advance.
Also, on the topic of "how much of X6 was intentional?", I submit to you the alleged issue of permanently losing power-ups. Basically EVERYONE who doesn't know their way around X6 bitches about this despite the fact that all of the "essential" parts are located in areas where they cannot be lost (the most important part that you can permanently lose is Speedster; which is ONLY useful in aiding physics exploits that you have absolutely no reason to be attempting once you get Hyper Dash). In X5, the aforementioned oddball Zero work-arounds for an extra Heart Tank or two often require power-up parts that you have a less than 50% chance of ever obtaining, and that you may deliberately want to forsake depending on your preference. X6 has no such restrictions; whatever you outright NEED is always available, whether you found it yet or not.
I think this issue has to do with expectations of the game.
The problem with X6 isn't that you can't obtain the tools necessary to advance, the problem is that these tools are optional/miss-able and that the game doesn't inform the player in some shape or form that they are necessary or that they even exist to begin with. Even if the player does have the upgrade, it might not even occur to them that said upgrade is necessary to pass said obstacles. A personal expectation I have, and I'm sure many people share, is that any stage within the X series can be cleared no matter when or how you entered it. As far as I know, besides Magnet Beam in Mega Man 1, X6 is the only non-spinoff game that I can think of that actually requires you to quit the stage and backtrack because you weren't properly equipped enough (or in Gate Lab 2/Shadow Armor's case, "you dun goof'd").
You can argue that this sort of backtracking and searching for the upgrade you need would be applauded in games like Metroid or Castlevania (Metroidvania). But again, in those games I expect to do those things while in X6, I simply do not. The Metroid-style game works because they operate in a large open world: backtracking doesn't break the pace the game, it simply requires you to turn the other direction. Mega Man X doesn't work like that: you choose a stage and go from start to finish. ZX Advent is known to do this in 2 parts of the game, but this was more acceptable because, despite having linear-styled stages, they were connected enough to give an open world feel while also not actually making you backtrack much at all by teleporting you to where you needed to be. Even Mega Man & Bass, during the special weapon requirement stage, gives you a teleporter back to the stage select.
If Capcom wanted me, the player, to have a change in those expectations/assumptions while playing the game, they either should've been cluing me in with Alia or, like you said, give me easy access back to stage select. And yes, I am very well aware of the fact that you can return to title screen and load previous data. However, that method is extremely roundabout and carries the implication that you are quitting the game, not that you simply want to return to an earlier point. In fact, I don't even think Capcom had this method in mind: the spiked walls seem to carry the message "if you aren't well equipped, kill yourself here so you can return to stage select". I am confident that the idea of returning to the title doesn't even occur to most players because that option wasn't intended to solve requirement issues, it simply exists as a "soft reset" that many other games utilize as an alternative to hard resets. In X4 and X5, they were mainly a tool of convenience to restart or load another data; it just so happened that they also offered to go back to stage select, and this was probably meant for players who changed their minds about quitting. 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.
Now let's just say that Capcom DID intend the title screen/load previous data to be the solution for being ill-prepared. Then I ask you this question: What is the point of lives? And by extension, what is the point of the EX Item? Player Rank is determined by Souls, which means accumulated damage is simply for record keeping and has no gameplay effect on the player. You can keep continuing from the same checkpoint even after getting a gameover. So then, how do lives benefit players? The answer is they don't: they simply deter a player from rushing each stage for quick upgrades. But that doesn't actually prevent players from returning to stage select, it just makes it more tedious to do so. If you view it like this, then you can pretty much call out Capcom for being idiots because they could've easily been much more straightforward about it: if players are to return to stage select, then they are forced to give up all the upgrades they acquired throughout the run. Otherwise (which is probably the reality, especially
when you add EX Item to the equation), you'll notice that Capcom just blindly followed its own convention without actually thinking about why they were implemented in the first place, which was that lives were to aid players in advancing to the finish. And yes, X5 is guilty of the exact same thing, which serves as even more proof that Capcom didn't actually know what they were doing because they just did it again.
EDIT: I've been making numerous edits to this post in order to clarify myself, but I think what Egoraptor said
summarizes the point well: "Castlevania feels well thought out, it feels planned and complete. But Castlevania 2 feels like a [tornado fang]ing mess". Of course, replace Castlevania 2 with X6 (how ironic that the analogy that was attempted to be made was instead interchanged for the other).
In case people are wondering why such a long wall of text was necessary: I made this same exact argument years ago, and everytime I tried pointing something out, counterarguments made against me (that were usually taken out of context) missed the point entirely: 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.
In terms of good open ended design, games like Super Metroid and Zero Mission are much better examples because they both are approachable and reward cleverness. In terms of challenging design, games like the original Castlevania and Hard Corps Uprising are much better because they are actually cohesive and consistently fair. On no respectable scale does X6 actually compete as a top contender, the only notable gameplay merit it has is being so frustratingly hard in that its completion is considered an achievement. (By the way, I am referring to the game as a whole: X6 of course does have its moments of legitimate design. However, it cannot be ignored that X6 also has its equally illegitimate moments of artificial difficulty and situations determined solely by luck).