Zelda has to approach ZSS because ZSS has more range and a lot more speed in general. She has a few safe options against Zelda's shield and can actually reliably shield poke with enough pressure. Maybe I just suck, but I'm certain ZSS is Zelda's worst matchup by far for many more reasons besides this.
1) None of this makes Zelda have to approach when she is in the lead (OK, big deal, ZSS is shield-pressuring you, why will that coax you to approach her? she's obviously the one doing the approaching if she's pressuring your shield trying to get you to come out). If you're in the lead there's no reason to safely pressure a shield. You can just wait, or move around and assert stage control. Falcon doesn't have to approach in the lead. Neither does ZSS. Neither does Zelda.
2) Falcon's jab has *way* better pressure than anything ZSS has, including her n-air. The thing is crazy ridiculous. Not only that, but empty hop from Falcon is scarier than empty hop from ZSS because his dash grab is way better due to not being a tether and because he's faster on the ground.
Zelda is generally going to approach Sonic because sitting by waiting for Sonic to run up to you and attack you will mean he has a free chance to either grab or hit you, and even if Zelda predicts properly, he can move right back out to safety.
You can replace Sonic in this sentence with Falcon and it will still hold true.
Except that I disagree that Zelda needs to approach Sonic if she has the lead. I agree that she shouldn't remain
stationary, but there is a difference between
moving and
approaching. Sonic is not threatening from long-range. He is threatening from midrange. The same is true of Falcon, but Falcon has more options in midrange, which makes him harder to predict.
If Zelda is in the lead, she doesn't need to approach Sonic
or Falcon, but if she did need to approach one of the two (in some other dimension where smash 4 is a different game), it would be Falcon, not Sonic.
You boiled Falcon's options down to dash, grab, jab, and aerial (which is not representative of his actual options, because the response to pivots/crossups, for example, is way different from the response to forward-facing approaches, but let's go with it). If that's the case, then Sonic's options can be boiled down to spindash/dash, grab, and jab. Notice how they are the same, but Sonic doesn't have "aerial" there? Because his aerials aren't as safe as Falcon's on shield. From where I'm standing, I see Falcon as safer on shield. They're both fast, but Falcon has more range on his jab, and aerials that he can use on a shield. What does Sonic have to compensate for that? How is Sonic safer?
And, if you say Falcon is lacking when he's at a disadvantage, would that not mean he's much easier to deal with than characters who are problematic for Zelda at all stages of the game, even when she's ahead? I'm not saying that you said this - I'm just trying to tie in my original point with our discussion.
Zelda is good vs. Falcon for the same reason that everyone is good vs. Falcon: he sucks in disadvantage. He has one of the worst recoveries and his n-air is hard to use to escape juggles. Sonic is harder for Zelda than Falcon, yes, because Sonic is good in disadvantage.
But saying that Falcon has to approach Zelda and that Falcon isn't safe in neutral? That's more like misinformation/misguidance than anything.
edit: pfff quote tags