Baby Bean almost seemed to be older than he really is for some reason. Steve Whitmire's voice was already high pitched, young, and cute when he performed Bean. I don't think Dave Coulier captured that naivety in his portrayal of Bean. I have yet to decide if that's just a character thing or a voice thing.
Seems to me, Baby Bean was unsure of himself and constantly depressed... and somewhat of a loaner. I am reading into it too far, since clearly the writers didn't know what they wanted to do with him. He asserts his cuteness a bunch of times, but somehow I think he doesn't know how to make people like him. In "Whose Tale is it Anyway" he actually sings a song about how he wants to make everyone happy at the cost of his own happiness. In fact, that was the only episode where they gave him a character instead of hand me down lines from another character.
It's possible. Take the characters on 'A Pup Named Scooby Doo' for example (young Velma being more quite and laid back, young Daphne being a spoiled brat, young Freddy being a moron). That's pretty common on TV shows with younger versions of characters. I guess it makes things more humorous.
Freddy wasn't just a moron... he was a VINDICTIVE moron, constantly framing everything on his nemesis Red Herring.
Of course, other than his leadership skills, his adult counterpart lacked personality most of the time. The movie version, seems like Freddie Prinz Jr. played him as the "Pup" version... where as the What's new Scooby Doo? episodes made him a little more personable, but like his older self.
Gonzo also indicated a slight comic crush on her in TMM, "I'll eat with you Miss Piggy!" And also in Season 2 or 3 he goes to her dressing room to inform her that he's over his crush on her.
Without a doubt, that's where the idea came from. I feel the Gonzo crush on Piggy in TMS was something that came out of the character BEFORE the chicken attraction (which really started out with Dave's adlib "You didn't get the Part. Nice legs, though.")
However, it seems the one difference Baby Bunsen has over his adult self is the know-it-all factoid spewing in certain episodes... what's the one where they pretend to go to outer space, but it isn't "From a Galaxy Far Far Away?"