There's a lot more that goes into the game than damage building. Spacing/zoning opponents out to get safe damage and setup opportunities to build damage at all, avoiding damage so you keep the lead and don't get killed, finishing off stocks. etc. If pure damage building was what mattered most, Brawl Sonic would have been one of the best characters instead of a mediocre one, and Brawl Snake wouldn't have been that good.
For your example, if you made Needles, Vanish, and Bouncing Fish bad, Sheik would absolutely not be top tier anymore. Those are by far the most important moves in her moveset, and are the biggest contributors to why she has been such an OP character. Needles let her zone out everyone despite being a rushdown character and are used for important kill setups/gimps, Vanish gives her an absolutely free recovery and a really effective KO move to finish off stocks early, and Bouncing Fish recovers, finishes combos, kills, and gets Sheik out of bad situations for free.
And... what happens when you take away the quality of her standard attacks? She drops several tiers and is probably even worse off than she would've been, because a bigger bulk of her attacks (such as her Fair) are suddenly much worse. Bad specials can cripple characters, but bad standards are also likely to do the same if not worse.
Yes, nerfing Luigi, Rosalina, etc. out of their good specials would drop them in tiers. I'm not denying this, but it'd be even worse if they lost their quality standard attacks. Luigi's more likely to maintain a mediocre C tier status without good specials than he is without good standards.
I'm not saying damage building is THE most important, but it's up there, and characters would be nothing if they had an assortment of 11 or so moves that suck. That's my point. Standards are more valuable to an arsenal for a character's mainstay in the meta, barring exception cases. (Duck Hunt, Link, Young Link, Mega Man, Robin, etc.)
But at the end of the day, both are integral to making a character work. However, standard attacks are, as far as I can say, far less likely to jump a character multiple tiers than several buffs to standard attacks. Wii Fit Trainer didn't make 2 spots in Top 32 at EVO on Jumbo Hoop alone. It helped, but there was already something to her character people missed hidden away in her wonky hitboxes.
That bad recovery is Falcon's biggest flaw and is the main thing holding him back, especially in Smash 4 where bad recoveries aren't the norm. And Falcon being "combo food" comes from, besides falling speed, him lacking specials that gives him protection when sent into the air. Time to bring up Smash 4 Sheik, she's a fast faller like Falcon who lacks aerials with disjointed hitboxes, but why doesn't she get hit anywhere near as hard when sent into the air? Because of Vanish and Bouncing Fish getting her out of such situations. If you made Falcon Dive a good recovery move somehow, and turn aerial Falcon kick into a move that could more reliably get Falcon back to neutral from the air, Smash 4 Falcon would definitely become a top tier.
For Melee Falcon, I already explained: If Falcon's in a recovery position, he still has the disadvantage of having to secure a position in which he can build momentum. He relies on momentum, or he's dead no matter how good his recovery is. No characteristic specials in Melee's context could possibly be better than the speed and versatility of his SHFF aerials. His weakness is in his playstyle, and the capability of the player piloting him. He's a very technically demanding character.
That linearity is a result of specials that give them little additional effective options and that fail to cover the holes in their offenses and defenses.
I mean, there's nothing really
there for them. Ice Climbers really rely on wobbling, and I don't think better specials could give substance to their standards. They're low-tier material in P:M without wobbling and chaingrabs, as an example.
Yeah no, this kind of attitude is what leads to inadequate information being given and people saying what amounts to bull**** (e.g. Mii Swordfighter is totally bottom 5 still!)
But... it's pretty much true. If you're light and floaty, you're in the air longer. If you got knocked around, you're still in the air for a longer amount of time. Almost every floaty character in the game has compensating aerials, including Samus. Zelda's aerials are all, sans her Nair, pseudo-knees with a lot of lag and little reward.
Villager is another good example. He's floatier than Zelda is, but he has good aerials that cover his movements. Only a character with movement like Sonic can feasibly pull off stall with hit-and-run tactics based purely on his absurd mobility. Other characters need aerials to cover their lengthy aerial times.
If Din's Fire was a good projectile that could be used to effectively zone with, it would mean opponents would have to approach Zelda. Which means Zelda could actually utilise her moveset defensively like it's tailored to. It would mean her poor mobility is a minor annoyance instead of being crippling (poor mobility hurts you a lot more when you actually need to approach and chase people; see Brawl Olimar for why poor mobility doesn't matter when you can camp everyone out and hit hard when they get in). Suddenly Lightning Kick won't be so bad, when you can afford to throw them out, and hard hitting moves that don't really combo would become a lot more meaningful when your opponent is soaking up more passive damage and being more pressured.
Her defensively tailored moveset is garbage. See: Every other stall-based character in the game. Her endlag on Lightning Kick would not suddenly make her able to toss them out like Jigglypuff Bairs, because that lag gives an opponent the opportunity to move in. Din's Fire would need to be
absurdly broken in order to make her all-kill-move-aerials (sans Nair) viable, and at that point, Din's would be doing most of the work and would be an exceptional case ala Diddy Bananas in Brawl.