There's another of Link's issues, which TL also has to deal with.
Lack of OoS options. As said before, Link/TL's fastest OoS option is frame 9, with 1 frame of jumpsquat if done frame perfect and 8 frames for the first hitbox of aerial spin attack to come out. This leads to issues.
1: Frame 9 punishes are slow for how good shield stun is now in Smash 4. A lot of aerials are hard to punish with frame 9 moves, unless they are badly spaced.
2: You're doing an aerial spin attack...That's insanely laggy if you miss. That's like doing it on Mac, you're dead. I'm pretty sure Aerial spin attack has the same type of FAF in the air like it does on the ground, which is 42 frames. 42 + Fall speed + Hard landing of 5 frames = Biggest window for a punish I've seen ever.
OoS Up Smash would be safer, but now you're at frame 11-12. Which is on the level of OoS Jab.
There's mobility, and then let's get back to the fact Shulk even with Monado shenanigans is one of the worst characters in the game and that Yoshi, with some of the best mobility in the game, wins next to nothing notable.
And that Luigi with some of the worst mobility specs in the game overall, had some great tournament results before patch changes.
Link also has item tossing (and Bombslide), several aerials with comparable safety on shield as ZSS N-air which CAN be used rising in punish situations, and is much less finicky with Rage compared to ZSS.
Link might not move fast in the air, but he benefits from a strong run pivot for weaving on the ground, and controls a huge amount of space with all his moves. And the grab simply cannot be disrespected in neutral, especially when nobody wants to actually jump against Link in neutral.
Shulk has to deal with subpar mobility. He gets a boost in one category, loses even harder in another. He gains it for 16 seconds, loses it for 11 on CD. In a 6 minute game, this leads to 13 uses of Speed if used every second that it was available, or jump. He has over 2 minutes of not having the Monado up. This doesn't fix the problem, it just glosses them over.
Yoshi has the mobility, but has other issues he has to deal with, which is why he doesn't get his results.
Luigi had the best throw combos in the game, killed you off a grab at 90 with zero counter play. His mobility didn't matter as much, not to mention his ground movement is still better than Link's because of how good his initial dash was, coupled with his amazing dash grab game.
Ness' mobility is an issue of his, but he also has 2 of the best OoS punish options in the game. Frame 6 OoS N-Air that does 11 damage and can be used rising, and frame 6 grab OoS that will kill you at 80-100.
Does Link have none of these?
No. He doesn't.