I've been lurking in this thread for a long while since the last time I posted, so I figured I might as well address something that has been bothering me for the last few pages or so. Just going to briefly go over what I think about Zelda and whether or not her average at best mobility is an issue for her.
No, I don't think this is her only real problem or necessarily her single worst trait, especially now with how her tools have shifted from previous games (Phantom), but I do think it's a weakness nonetheless and some of the arguments against it confuse me. I'll just cover a situation with a character I'm familiar with to make it easier to explain.
Greninja and Zelda. In every aspect of movement stats, Greninja outclasses her. He has more range, a quicker projectile for its distance, and the ability to play at mid-range and bait out options for him to whiff punish simply due to the gap in movement.
Things like Displaced Phantom or Nayru's among other tools to deal with opposing projectiles or work closer towards cornering and cutting off escape options to slow the pace are helpful, but I what I feel she lacks is solid approach tools (especially when dealing with the faster characters in the game) and the frame data/mobility to consistently zone them out alongside it. When she can't establish enough space and time to keep enemies out or if she has too much space and her super long range pressure isn't exceptionally potent, it can be hard. I see a lot of Zelda players reference MUs like Greninja, ZSS, Shulk, etc and they all have very similar things in common.
If Greninja for example gets a sizable percent lead or a stock advantage as to where Zelda is forced to approach, this is where things get tricky. Phantom is great and ties her kit together for the most part, but due to its design is exploitable. It blocks projectiles and when charged into the final few stages has an overhead/uppercut slash that hits the lower platforms of most stages, but depending on how much distance you want to cover for the attack itself so you can actually dissuade the idea of traversing on platforms, it has more startup on it allowing for counter play and she has to be closer to make use of it to hit people (one example where closing the gap faster would help). On certain stages with higher platforms for avoidance or with characters who have high jumps, waiting it out and/or circle camping by using the platforms as a movement tool has a strong effect.
Fully Charged Phantom has the best hitbox for reaching platforms and sometimes even catching the startup of jumping, but this can't be spammed as effectively due to the move's design. Even if you are displacing it every single time to avoid getting the starting charge hit by a projectile and the move fizzling, in the final stage, because it remains on the field for a little while longer after swinging, you can't throw another one out right away and thus it has a natural cooldown. If Zelda is being pressured a lot in Neutral or is trying to use it for zoning purposes, they might want to release the overhead swing (or earlier) so they can pressure back with it sooner, but this has its own share of issues (less distance and power for example) and she is put in an awkward position in certain MUs. Having to rely so much on this move can be troublesome due to the startup and endlag that allows for Whiff Punish opportunities; it definitely can't be utilized mindlessly.
Greninja (similar to ZSS) has a Top 3 Jump Height and enough Air Speed to make use of it well as they move from platform to platform, up and down and back to the ground again with Fall Speed as well. This adds to their mobility and separates the MU from someone like Mac (who has a huge ground speed advantage over Zelda) from doing better than they do (alongside other weaknesses of course). Besides not having any range or projectiles, Mac can't truly camp her out. He can't jump into the air well, so he has to make his way through her zone, and in this game especially, it's way harder to do. She might find it annoying if Mac has a lead, but she gets her chance when Mac has to go through her because at least if Mac hits her shield, he's unsafe and she can punish OOS and Mac has to resort to rolls and whatnot because he can't run past anymore. Greninja and ZSS have moves with safe pressure against her on top of having to almost never need to cross her up grounded. If Mac gets cornered, he's stuck, but Greninja and ZSS just jump over her or to a platform and reset. Zelda has average Air Speed and below average Air Acceleration. When she has to jump to chase people weaving around her because her projectiles aren't enough and Farore's is too risky to use to catch up, this is where it can fall apart at times and it can snowball out of her favor as faster characters whiff punish laggy attempts to chase, she gets put in disadvantage where she struggles to land or regain center stage, and the percent gap just increases even further incentivizing the idea of going right back to playing lame.
What I will agree with is that this weakness isn't as pronounced as it was in previous games, and Phantom actually has a lot to do with it. But having a Punish Game is helpful too and so is the natural mobility buff the engine transition provided. Zelda isn't a great character in Melee and Brawl and for example, her MU vs Fox is what you expect in agreeance to this. However, due to the contrast in tools/punish game, it plays out a little differently (although it's still rough in both of course). In Melee, Fox camps out Zelda with Lasers and runs the whole time, but if Zelda finally catches Fox, she at least gets to Chain Grab him to death. In Brawl, she struggles chasing Fox as well, but then she closes the gap and gets something like a grab...and that's it. Zelda gives him a measly 8% while she took 60%+ trying to chase him across the stage. She has to try and catch someone for subpar damage vs someone who's faster and has an easier time doing damage in comparison.
The issue is no one is consistently playing super lame like this, but if they want to shut her down harder and not have to deal with her better punish game in Ultimate so they can win, they would. I have no remorse with timing out opponents if I see the clock is winding down enough. Also please don't misconstrue my example of one perspective to say that I am implying there is zero counterplay on her part for the above, just wanted to outline why it's difficult and why sometimes it is not a trivial issue. Not saying anything is literally impossible, just indicating why it can be uphill.
There is definitely more than one way to solve this problem though, but I feel like everyone is going in circles with the arguments. Most of y'all on opposing sides seem to agree with the majority of concepts, but the nitpicking isn't helping either of your cases. If Zelda had an even stronger punish game, the ability to trap certain opponents in disadvantage longer, or if Phantom had less startup and cooldown to where she can consistently pressure from a long distance with it, then yes her overall lacking mobility would be less of an issue as she'd have adequate tools to play around it. And in some MUs, I'd say she does have enough tools to play around it, but I fail to see how in a Platform Fighter like Super Smash Bros. how a movement buff wouldn't be helpful to her, especially when on paper her stats for that category is in the middle of the cast across the board.
Not every stat increase would be drastically beneficial to how she wants to play or what she'd get off of it with her current tools, but some of it would just be objectively a buff and I'm sure in certain MUs she definitely wouldn't mind having it. Everything else about specific and objective stat increases and how it wouldn't hurt to have a rise in some areas I think Krysco covered pretty well.
Even just very surface level stuff like having a little more speed to catch landings with for example I can't see being a bad thing. Movement isn't simply just about running left to right because this isn't that type of game. It's why I feel one could argue Greninja has the best overall mobility even still. He may not be #1 in every individual stat, but he ranks in the Top 10 for almost all of them. For a quick reference, this reminds me of hearing Venia talk about Greninja and Fox in the previous game. While some stats have shifted from S4, Fox still has a very slight edge in Walk and Run Speed. However, Venia liked to compare Fox's movement to a Bullet. Fox is fast, but only going one way at a time. If he's running, he's only going horizontally fast. If he's jumping, it's just quick up and down due to his Fall Speed. Fox has slightly higher air speed than he used to, but still not near Greninja's level so all the in-between movement isn't as crisp. Greninja however can go every direction and mix it up as he pleases. His jump allows him to reach the top of the stage and his fast fall speed allows him to reach the bottom just as effectively (Even Dair dives him to the floor should he need to and Hydro Pump, Shadow Sneak and Shuriken give him varied Special Mobility which is unique in and of itself). His Air Speed allows for better platform camping as he darts around the stage and not everyone can chase him super well when he commits to it.
This ties into all aspects of his tool kit as he uses his low profile, range, projectiles and speed to control the pace, stage control (avoiding getting cornered), and how much he needs to actually shield things. It's why it pains me to see Greninja players not abusing this all as much as they should be and refusing to go passive and extend a lead when they should, but hopefully that'll change in the future.