Well first thing I'm going to say is yeah it is.
And yeah you did have to write that up.
I agree that Sheik is hurt less on static stages compared to Falco, but I want to know what stages you have in mind when you made that statement.
I don't think Sheik gimps Falco really well at all compared to other characters. Every character should be able to kill a Falco that's forced to recover with firebird, but Falco shouldn't be forced to do that unless there's a case of bad DI or bad buffering.
Falco having an easily punished recovery is a thing of the past against most characters. Sheik is just your average edgeguarder against Falco unless he makes those said poor decisions like ending up recovering with firebird.
Needles do beat phantasm, but don't forget they're shot in a straight line, meaning they're easy to get out the way of.
Her F-tilt lock is both good and bad against Falco because it starts at about 30%. It basically means that before that, any SDI (or normal DI) downward results in Falco shielding the ftilts. At about 30% Falco knows to expect the F-tilt. This basically means that if Sheik is fishing for the f-tilt too much, she's going to take a lot of damage just trying to hit with the lock because Falco is playing a good keep away game.
Falco does have killing power. His problem has ALWAYS been landing the kill move. Which is not so much a problem in this MU. Neither Sheik nor Zelda have very much that is safe on shield from an OOS up smash, and neither of them are the heaviest characters. They both have very linear recoveries as well meaning a bair offstage is a very viable option to kill with, or uair.
Falco's ftilt. Sheik can't even do much about this even on shield.
Falco's jab. Faster than all of Sheik's moves.
Falco's CG. Especially effective because of Sheik's weight/falling properties. Spike you on stage > Gatling combo puts you at 70/80 percent in one chain/combo. Few lasers and jabs and you'll be in kill percent. If you decide to actually change to Zelda to get the kill like Nova suggested, Falco will have an even easier time landing his kill move.
Remember that Zelda's Fsmash can be SDI'd.