To some extent they should, I think at the very least you have the tennis racket and let him whack a ball around. And I believe his air swimming abilities from the Tennis games would make for a great recovery. But I would much prefer that on the whole, they let Waluigi's dynamic character dictate the moveset over simply reaching for the "canon" references. Waluigi is both extremely defined as a dastardly, cheating sore loser but also a pretty blank slate in terms of what you can DO with him.
Anyone in the Mario universe can swing a bat and ride a go-kart. What is unique to Waluigi? In my eyes it's his characterization as a cheater. Waluigi is essentially a cartoon villain - by design of course, he looks just like D-ick Dastardly (they censored me for this lol). And remember those amazing Mario sports opening cutscenes? He and Wario make for such a hilarious villainous duo. Probably inspired by another duo of wacky animated schemers...
<-- Tonzura and Boyacky from Time Bokan / Yatterman.
So let's lean into that - for his forward tilt, maybe he pokes you in the eye as if he was one of the Three Stooges. He air swims upward like Lupin the Third and at the peak, if he hasn't grabbed the ledge, wiggles around frantically and plummets straight down like Wile E Coyote. And he embodies an unpredictability and outright strangeness, getting hit with some of Waluigi's attacks should feel unfair because that's exactly his game. Like an Up Smash where he contorts into the pose of an upside down L, with a random spike on his fingertips. You'll be left wondering what the hell happened and feel cheated out of your win, and Waluigi will be laughing all the way to the winner's podium. Just crazy stuff like that, yknow? Really just spitballing all the wackiest ideas I can think of. And why not, let's give him that burying stomp that has become so iconic of his presence in Smash by now.
Smash doesn't get to simply let a character's personality guide their moveset in this way very often and I think it would make for a really fun and refreshing character. Not without his references, but there's so much untapped potential with Waluigi and Smash may be just the place to bring it out. That's what is compelling about him to me, at least.