It holds up quite well, but honestly, it's just aged really poorly. There are a bunch of balance issues with the game, and it's super outclassed by the later Smash games.
The infinite hitstun and lack of DI makes it somewhat polarizing. Sure, free zero to deaths is very fun to perform, but that is until you are the subject of a zero to death yourself.. There is really no other Smash game here you can string literally everything into everything, so it's unique in that regard. I honestly quite like this, but some people don't.
Now, for the things holding it back from me playing it by myself. There is sadly a lack of things to do by yourself, so the single-player aspect is practically non-existent. Also, the graphics, in general, have aged VERY poorly. The characters look kind of like something from a direct-to-video CGI film that was crudely animated with motion-capture, as the animations and models just look very choppy (DK being the biggest offender). Also, Smash 64 Kirby was one of the biggest offenders of "low-effort, huge payout" in the series, with dumb moves like Dair and his infamous Up Tilt. And the fact that zero to death combos are just so easy to perform now makes them a little less impressive sadly.
Overall, a good introduction to the Smash 64 series, but it really is outclassed by the later games. Still, nothing is more enjoyable than a nice zero to death combo, so if those are your favorite thing to do, then this game is for you. It's not my least favorite Smash game (that goes to Smash 4) but it's just the one that's aged the worst.