Interestingly, I feel like in "Big Bang Theory", the opposite happened -- the first few episodes, the characters were almost entirely a bag of stereotypical "geek" quirks; they slowly became more human as the show went on.

I think I remember in an interview one of them saying that filming before a live studio audience actually helped with that -- you got immediate feedback about what the audience thought of the characters and the show; and people are just more interested in characters they can identify with.

It’s driven by the nature of jokes in a long-running medium. Jokes both require and create context; this joke’s punchline is that joke’s setup. If the setup isn’t rooted in the current context, it’s nonsensical. If the punchline is in current context, it’s boring.

It’s easy for this process to feed back, especially with large casts of characters. I heard a writer once talk about “protecting” characters from some jokes, I believe to prevent a process like this.

I believe it’s more about available time. When you only have 20ish minutes to pack as many gags as you can, and the narrative setup is fundamentally immovable (i.e. episodes are entirely self-contained, there is little or no substantial continuity), subtlety will soon go out the window, and characters will become stereotypes who exist to trigger jokes.

Also, that sort of narrative setup tends to accrete over the years: if you’ve seen Barney being the idiot drunk for 5 years, that’s where your mind will go as soon as he’s in the picture, even if he’s had the occasional redemption story (he’s a poet, moviemaker, etc).