Well, honestly, I just don't see how having items on would make them any less broken than they are.
Sonic, Yoshi, and Jigglypuff need a word with you. High ground or air speed can be a tremendous boon depending on which items are active. It's also a whole new batch of strategy and evasion to contend with when you're on the wrong side of an item battle.
It's not just items, either. It's also terrain, it's also stage hazards, it's also free-for-alls over one-on-ones, it could be team battles, and occasionally it's even the 2.0 damage ratio. These are all things that the tier list ignores, and which otherwise play a large part to your average Smash gamer, and they can RADICALLY alter the game's balance.
Bowser, for example, has a "Win Button" in 2.0 Damage, that being his Flying Slam, which will guarantee a KO in all but the largest stages (being a grab attack, it's also unblockable). He generally blows otherwise. Larger characters in general (Snake and Dedede) also have a harder time in 3-or-4-players matchups due to being easier targets, doubly so when somebody's aiming a throwing item at you.
Yoshi is great around slopes, seeings how his eggs, roll, and drop moves allow him to easily attack at odd angles. He's also good for maneuvering around platforms thanks to his high air speed. And the flinch-resistance of his second jump helps him to escape hectic areas.
Also, going into Final Smashes, the Landmaster's effectiveness varies GREATLY depending on terrain. In Final Destination, Battlefield, and the like, it's pretty much guaranteed KOs. In Yoshi's Island Melee, or Spear Pillar, it can easily be laughable.
As far as Final Smashes go, the same rule of distribution applies. I mean, you've got great ones like Sonic/Space Animals that can net plenty of KOs, but as a Mario/Kirby user you feel gypped. With Mario's it ends up being a very straightforward move that everyone can react to and evade on release, and with Kirby's you can literally spot-dodge at the right moment and avoid damage altogether.
Super Sonic I see as compensating for Sonic's generally low power otherwise; there's a reason not every character has it. It's also one of those moves that the user has to know what they're doing; sensitive controls makes for easy spot-dodging if you don't think to attempt hovering. Most other Final Smashes are devastating but avoidable if you're good enough. I've already used the Yoshi Bomb to dodge Marth's Critical Hit, and damn that felt good.
They are SUPPOSED to be overwhelming, but they're usually (not always) not outright impossible. ROB's pisses me off, though.
There are some that really feel underpowered, and I agree that Mario is one of them. Bowser, which I often rant about, is another, and Pit's leaves him pretty open as well. Seems like the early characters got jiped and the more off-the-wall late additions got the crazy power.
Mewtwo wasn't even close to anyone else in the game in terms of execution, and he still got axed anyway. How Lucario's supposed to be a replacement is beyond me.
They're loner semi-humanoid Pokemon, they have chargeable projectiles, a similar forward smash, and command some glowy supernatural power. They're pretty much it. The general "fighting style" of Mewtwo is
NOTHING like Lucario's. If anything I think Zelda is closer to Mewtwo in terms of play style, but there truly is no substitute for him.
Keeping it on topic, I did like how despite the crude advantage the higher-ups had in Melee, bottom tier guys could still compete. L-Cancelling made Bowser's aerials far safer and kept you from getting whipped too badly, though his weight made him easy combo-fodder. Kirby had his trademark Kirbycides which allowed him to net surprise KOs (at the expense of his own life), and pretty much anyone was useable. I actually don't like Melee's high-execution requirement in higher levels of play, though. L-Cancelling should be automatic (be honest, is there ever any reason to not do it?), and while stuff like Wavedashing is cool, doing it all the time as a means of travel seems pretty cumbersome. I play Street Fighter competitively, and TBPH Melee seems far harder in terms of execution at a high level.
Wave-dashing was an accident, like the Minus World of NES days. Agreed on L-Canceling; there's no point in having a manual switch to recover from your own moves. If it's depending on when somebody hits you (catching yourself on the ground after you're sent flying), then that's a whole other story.
Damn you! 
I missed you, too, 'maru.