I was really surprised he was cut because Sakurai was actually going to add Wolf in Melee but he thought he looked like a Fox reskin so he added Falco instead for looking different and having a similar height/build. But this makes Sakurai a hypocrite because he added Doctor Mario because he thought Wario played too similar to Mario. So not only did he add a newcomer that played like a character, he looked just like him but in a doctor cosplay.
I think a possible reason Wolf was cut might be because Sakurai had no idea what to do with him. Think about it, Ganondorf became a Captain Falcon clone because Sakurai ran out of time - his victory animations and trophies are leftovers of a sword-wielding Ganondorf.
Wolf was supposed to be in Melee, but was dropped because he would have looked like Fox, but with an eyepatch. Now, look at Falco's move set in Melee, Wolf would have had that set. Sideways Blaster-grip is like a nod to gangsters, Wolf being heavier would make sense since wolves are much larger creatures compared to foxes, and a similar idea would lead to him being slower. Welp, with a couple of changes like higher jumps, voice clips, and a different head we have Falco.
Then you go to Brawl where because of recent Star Fox games, Wolf looks much more distinguishable from Fox. Wolf in Brawl was a savage fighter compared to Fox and Falco, but Wolf wasn't really portrayed as a savage character in any Star Fox games. If anything, he was rough like a cowboy like in Assault. With the 64 remake, we have Wolf returning to a British-accented, cocky mercenary.
That means using Wolf's model from 64 with his Brawl move set would be weird as hell. You'd have this proper-sounding fellow who's fighting like a wild animal. Using his Assault model would mess with the theme of Star Fox 64 and sort of clashes with a space cowboy by having him as a claw and maul fighter.
How would Wolf from Assault fight? How would he fight if he was based on 64? For Assault, I can see him using a quick-draw for his Blaster where it has almost no start-up, deals a ton of damage for a projectile, but the ending lag is horrible. Melee-wise, he probably wouldn't use his claws or if he did, it'd be replaced by fist or open-handed attacks. For 64, I can totally imagine Wolf using boxing for most of his attacks - ironic if you consider Steve Fox - or bartitsu which is a combination of British boxing, French Savate, wrestling, fencing, stiletto use, and I think judo. It'd be dangerous, elegant, and probably underhanded-looking fitting an evil, British, space mercenary.
All of that would mean a large overhaul like what happened to Pit, Bowser, Zero Suit Samus, and is what's likely happening to Mewtwo. Damage values, different models, animation, and then you have to balance it.
Optimistically, Sakurai probably wanted Wolf, the Ice Climbers, and Mewtwo to return, but one couldn't make it because of hardware limitations, one had to be transferred and updated from Melee, and one would take too long to redo well. Sure, he could just make Wolf a freaking clone of Fox, but there would be no justification like with Falco who's a teammate of Fox, Luigi who's Mario's twin, Lucina where an excuse of passing down techniques and imitation can be used, or Dark Pit who's Pit's literal clone. Hell, you could justify Dr. Mario as a "legacy character" for people who wanted to play as Mario from Melee.