That's because... it's not Red. It's a generic Trainer loosely based upon him. He doesn't have a proper voice in canon. It's purely generic lines because he's a general player representative. He has barely a personality either. Various Manga and Anime do give him a personality, though.
The lines are presented even the same way as general lines throughout Pokemon's normal history for the player character. They could've had any design too, it's just Red was a more prominent one thanks to the anime having his counterpart in Ash(who actually does get mentioned in Smash). It also doesn't help Ash is a bit more known worldwide due to the Anime also appearing first in some countries.
Whereas some are outdated, Pokemon Trainer is one of the ones who kept being accurate due to being a Player Insert Character design here. He was the first proper Avatar character playable in Smash(where 4 added more, as did Ultimate). It would've been more interesting if he was actually Red, though. But sadly that's not the direction it went with. It's also much harder to go with a generic design visually when it requires a new model, and isn't a recognizable design. At least the one will make them think "this is Ash" or "this is Red", the most notable Pokemon Trainers in general. They did drop the ball in making it clear it's meant to be more of an Avatar, though. Which is unfortunate. The Trophies do make it pretty clear it's not a specific character(hell, they do the same thing with other protagonist trainers among the Trophies too, not even bothering with their names). Notably Leaf is the only one to actually get properly mentioned going into Ultimate. Red is still not used as a name even then, for whatever reason(likely due to the Avatar factor).
Trying to do both is detrimental, though. It just creates more pointless confusion. Despite being designed around the generic player avatar aspect, it doesn't fully act clear on it.
Oh, yeah, I forgot about the timing; Red didn't get personality till after Brawl. That could've worked having him properly be a non-Avatar if he came into Ultimate first, but the way it's designed works too. I would love to have more costumes based upon other Protagonist Trainer designs, though. 4 males and 4 females works wonderfully, and keeps the aspect of being an Avatar better than the current model. You don't really need new voices either, but that's because they're general voices anyway.