Today is my birthday, so I'm allowing myself to share One (1) mildly crack theory with barely any evidence (but I'm still slowly starting to like it):
I think Wally was made specifically for the Welcome Home show, and was never meant to be a real person to begin with. That's why he's so intent on being known as a puppet and "your best friend", because that is literally what he is within this context: he's the audience companion, he has to take your hand and guide you throughout Home, whether that is through the show and the everyday situations the neighbors get up to, or the hidden videos and audios that show you the truth of what's going on behind the scenes.
His character page says little information is ever told about him despite him being the main focus, because him having a backstory is unneeded: he has only ever lived in Home and has never been anywhere else. He learns things you would learn as a child, (colors, emotions, laughing, drawing and painting, the meaning of Christmas) as an adult, because he is first and foremost a character that was made to learn things in the show: so the fact it would be kind of impossible for him to live to being in his 20s without already knowing some of these things is completely irrelevant.
He does not know morse code despite that being the only way for him to talk to his own house because the show does not need him to know this nor for them to talk. (May be the same reason why Frank states he was the one to teach Home as wellā the show did not need Home to know it either, so it didn't teach him.) He is ambidextrous (seen using both of his hands for different things in different illustrations) because it is more practical for him as the main character to be able to use both hands, and thus he is able to. He is the shortest out of the neighborhood because being 3 feet puts him roughly at the same height as the child audience the show would have, and thus makes him more approachable.
His voice corrupts in the hidden audios while staying normal in the storybooks, because while the storybooks are a part of the show and its context, the secret stuff are unintended and are thus removed from it. The Echo/Specimen E video has Wally react to Frank trying to leave in a strange way because this situation was unintended and thus he literally does not know how to react to it (ā him using his catchphrase, "wouldn't that be the most?" despite the fact he actually rarely uses it in general ā Wally using more strength than is usual for him ā not outright telling Frank not to leave, nor why he shouldn't, but rather telling him to stay for the party's sake.)
If you remember back to posts from Clown's blog, (which yes I know Clown said not to use the posts but hear me out), this also tracks with some of the things he's said. Wally is most comfortable smiling because that's what's most convenient for the show. Wally has an "interesting relationship" to food and eats with his eyes because the show does not need him to eat (real life puppets cannot eat, after all), and thus he is not made to know the "proper" way to eat (with one's mouth). Wally understood art after he came to the neighborhood because he was always intended to learn it through the show.
I think the fact that he is able to see the hidden videos, access the website, call us and W on the phone, etc... shows that he is indeed a person, he's not "fake", he could get out of this context. (And well, there has to be some reason why he's reaching out to us; and if you believe him to be the WHRP's mystery collaborator, why he is trying to have us find the show.)
But with the importance he's been shown to give to his role (aforementioned "notice how he's still guiding us even now"), and to the Welcome Home show... would he?