Rain is not even a playstyle to begin with. Rain is nothing more than a boost to different playstyles since it is so versatile. I would also like to mention that wouldn't it be more logical to ban drizzle in general rather than a single Pokemon who is not even broken outside of rain? Also, it's not that we don't want to adjust to the metagame, but because wins or losses are decided by the pure team matchup is pretty bad.
But it's not determined by team matchup unless your team doesn't handle common metagame threats properly, which is a problem with teambuilding, not with team matchup. It'd be like building a team that couldn't handle stall last generation, losing against it consistently, then claiming that team matchup is a problem. You can't just ignore entire sections of the metagame like that and justify it by calling them cheap or overpowered. You could argue that team BUILDING is more important this generation than last; that's a decent argument. But I don't see how that would be a bad thing.
You're right that it isn't "a" playstyle though. It's a number of playstyles. But let's not argue semantics here. The point is there are a LOT of Pokemon that would not be viable if it were not for Drizzle, abusers and counters both. And I maintain that it doesn't make a lot of Pokemon non-viable in return, not nearly as many anyway. You'd hurt the diversity of the metagame by banning it. A lot more than you would by banning a single Pokemon certainly. The logic is simple. One pokemon, versus something like a half dozen, not to mention dozens of alternate rain abusing sets for Pokemon like Dragonite. I don't see what the hangup is here.
EDIT: @ undisputed
Well that's pretty much how I write. It's hard for me to be more concise without taking a LOT more time writing my posts. If people are interested in my opinion, they'll read it. If not, then whatever, their loss.