Then he's a pain in the arse to write for. Back when I used to read Avengers he tended to take long leaves of absence and only turn up for the big foes. They also made him more stupid than he was in his own book, which helped reduce his effectiveness - and of course for these reasons he's rarely in the leadership position, because when the team's big gun is also the guy giving the orders then that person dominates the book.
For what it's worth, I never bought into the "so-n-so it too powerful to be on a team argument", even when I was a kid. At the same time Thor was leaving the Avengers, writers were still to do stories with Superman in the JLA and Hulk in the Defenders. Hell, every other issue Wonder Man was saying things like "My fists hit like Thor's hammer!" He didn't have to leave cuz he was too powerful...
Good question. Maybe because Marvel wants to clearly tell us that Carol is Marvel's female face?
Why they didn't push Monica in the '80s brings up another point: Marvel in the '80s hardly pushed any solo character, except Dazzler. It was a team-dominated era.
During the Jim Shooter era of Marvel, there was a clear perception that team books were more popular than solo books. So when they launched new ongoings, they were usually spinoffs of existing team books like West Coast Avengers and New Mutants. Solo characters were mostly given limited series only. Even Wolverine, the undisputed breakout star of X-Men, whose first limited series was a huge hit, never got his own ongoing until 1988.
So the '80s were just a bad time to be a new character whose name wasn't Dazzler. Everyone was tied to teams and there were few solo ongoings for new characters. I think this is one reason why Marvel has a shortage of female stars: the '80s was a great era for female characters at Marvel, with Claremont and Miller and Stern and others creating new, stronger, more powerful women (or strengthening past characters like the Wasp), but none of them got solo series to establish them as stars.
Carol gets pushed in part because she got her solo series, in an era (the '70s) that had a lot more solo comics. So like She-Hulk, everyone knows she's an established star, even when she isn't doing anything.
Phla-Vell.... Sigh.
You can argue they're doing a pretty solid job pushing Carol. She's got her own solo book (even though it's not quite setting the sales charts on fire), and she's got a movie coming down the pike in a few years.
I won't say she's necessarily suceeded in winning over the readership, but I think marvel is doing a descent job pushing her.