Are character roles over-specialized in a lot of games?
This doesn't apply to all settings or all games, of course, but there are quite a lot both with an idea of "professional adventurers", or that at least have bands of people with such skills sticking together for long periods of time. In a lot of those, the game mechanics reward specialization. If you're a wizard, all your gains are about becoming a better wizard, if you're a fighter you become a better fighter, et cetera. Either that's the way it naturally goes, or doing anything else is suboptimal. More than that, we then get setting-related materials (novels, comics, etc.) where this specialization is reflected.
But is it believable? That doesn't seem how life would actually work in those settings.
If you have a classic mage, fighter and rogue team who go on a lot of adventures and spend a lot of time with each other, wouldn't they naturally pick things up from each other? There's always a lot of downtime, and people get bored and talk, and everyone wants to learn things that could be useful to know. Wouldn't the fighter tell the mage how to swing a sword right, or talk enough about battles they've been in for their partners to pick up some basic tactics? If the mage and the fighter watch the rogue search for and disarm traps enough, won't they start being able to watch for the most basic/common types themselves?
I feel like in any setting with professional adventurers, high-level pros would all pick up general adventuring skills in addition to their personal specialization. There are systems where this sort of thing happens, but it doesn't seem to be common.