Like Brock, they should have left years ago. But unfortunately we don't have that luxury with them. I honestly don't see why they feel the need to keep them on the show anymore. Ash's Pokemon should be evolving against regular trainers, not random Mecha battles with Team Rocket.
That's your opinion. Brock did leave once and he came back. I don't know why he came back but I heard something along the lines of people being disappointed or something so he came back(Not sure though). There are people who like Brock(Myself including), and if you don't like a character(Which is seems like you don't like Brock or Team Rocket from your post) then that's a unfair bias reason to want them off the show. I don't like Ash but I wouldn't want him off the show, I may not like his personality but he's still interesting to me, as are Brock and Team Rocket.
Team Rocket is the biggest source of comedy this show has. A lot of people like comedy so why remove comedy from a show when a lot of people like it? I find it always amusing with what Team Rocket does all the time, can't help but laugh. Maybe you don't find them funny but that's you and I'm pretty sure there are a lot more people who like Team Rocket comedy then people who don't like it.
Plus Team Rocket, just like everyone, has a goal. Their goal is to catch Pikachu(Amongst other things), so until they get it they aren't leaving. Also, Team Rocket as a whole was the main villain back at the very start and I don't think they have yet to disband or be foiled like the other evil Teams, and I think that's probably going to be the final moment for Pokemon overall. Ending a show like this with having the villain back from the start to end it off is a nice ending in my opinion(Although if that doesn't happen then that's fine too).
I know that TR are a source of humor for the anime but after so many season it's just terrible. I know they can find other ways to bring out the humor of the show without TR and their repeated and annoying gags.
That's your opinion. I still find them funny, as do others. A lot of shows have repeated gags, that's the whole point, to repeat and repeat and repeat and repeat and repeat and repeat...did I mention "and repeat"? Repeated comedy is common in a lot of shows and a lot of people like it.
They were in the Beta Artwork so it's a safe bet.
I really wish they'd have a permanant villian similar to Hunter J though. Team Rocket are hardly villians.
Well it depends what you consider a villain. No one in this show has come off as a villain to me. To me a villain is someone who wants nothing but chaos and wants the world to burn(And even in that case those villains tend to have some kind of mental problem which is the reason for it, thus making me still not see them as villains or evil). So I doubt I'll ever get my vision of a true villain ever, but Hunter J would be the closest to being a villain in my eyes(Although she's still not close).