I won't argue that one; I know I would love more aerial mobility. Wavelands off platforms & high priority only go so far. And it would buff her recovery immensely :/
Make an epic all encompassing 'how to win' flow chart
The problem with this is that it assumes Melee is figured out. Most characters aren't. Not completely. Just Falco.
@ Kaffei (and others interested in this)
Sheik doesn't have a move that really covers her front with decent priority & safety, and simultaneously encroaches a good chunk of the stage (which is basically the recipe for a quality approach - look at Falco's laser & dair). For Sheik, her high priority moves have high range because of how far she extends her limbs but don't actually cover that much space (because of low aerial mobility, her fair's arc, her bair not hitting on front, or her needing to stop to tilt [on a side note, ground moves are usually not so good for approaching]). Where Pikachu can lob some form of SH nair into dash dance camps to keep the opponent honest, Sheik really can't because she doesn't really have anything like that (aside from needles, I guess, but standing needles are a really defensive play by necessity). The closest thing she has is her own nair (and the obvious dash attack & boost grab), but her high SH cripples the offensive use of her SHFFL (but buffs its defensive use by expanding the reaction window on beating attacks). The result is basically that Sheik's offense needs to be controlled & paced because she can't threaten the whole stage - she needs to gradually take it. In this sense, her offense is kind of a spin-off of her defense. Only, you're proactively challenging space and then defending the new spot, rather than pulling opponents into your death wall. It's neat. Sometimes it's very effective.
If it helps, think of how Dr. Peepee's Marth plays. Only, you don't have d-tilt (which is honestly a big deal), you don't have dash dance (also a huge deal), and instead you have a plethora of slightly laggier but comboing tilts, a better shield game, a good WD back, a decent run > crouch, air needles (okay vs some chars), the ability to waveland off platforms into hard ranged moves, and a fair that's safer if you miss it (basically, a bunch of slightly worse but still respectable options). The overall principle remains the same - you're boxing the opponent into a zone and then picking off their options from there until you can just SH and cover their remaining options or force them to jump and tilt > fair them to death, etc.
Unfortunately, there are obvious drawbacks to this style (like with any style). The issue run-stop offense Sheik faces is that by moving forward you shrink the reaction window for timing her attacks. This can restrict the usefulness of the style against characters that can run her over in the absence of the reaction window (unless she starts flailing around and prays her limbs connect on the opponent, but at that point you're not playing offensive Sheik so much as you're playing 'please protect me from scary Falco my legs!', which is really just a bad version of defensive Sheik). That said, it's still a very good mixup (staggered Foxes can often by caught by this in my experience, and it's sometimes great vs slower characters like Ganon, Jigglypuff, and Peach) so you should know it just for that. And in my own experience against good players, some of them are just so much better at dealing with the standard Sheik that it's actually beneficial to play her janky offense as the main style.
It's a real shame that her only real way of attacking a big piece of ground is by dash attack or boost grab. While these are both strong options, they aren't good enough to be the foundation of a whole style (not anymore, anyway). So they're kind of demoted to "strong mixup". Which is alright, I guess. But they're nothing like Marth dash dance, Fox jump distance & dash dance, Falco laser, Falcon dash dance & jump stuff in general, Peach turnip > float zoning, etc. Y'know... the much better ground control & approach tools.