I only ban a teammates pick with people who try to play a newly released champion in ranked. No sir, not in my games with my LP on the line. You go to blind pick or draft for that.
I really, really dislike people who play weak champions in ranked, and the majority of the time this comes from top lane, but it's their choice and you just hope that you can end the game quickly. I hope you know though, that people do view you as a burden even if they aren't jerks about it. Making the game an uphill battle is just a sad choice, but it is your choice and who knows maybe you're the exception. 9 times out of 10 the laning phase ends in a predictable fashion in my experience.
You should realize that in ranked you're not just only playing for yourself, but your team. There are certain champions I reserve for ranked because I play them well and they are in decent spots to compete with the rest of the meta champions. I always keep up with the patch notes as well.
As for last picks, I don't really mind them because there isn't anyone currently that I feel I cannot deal with. From patch to patch that changes though, however usually someone 1st pick or 2nd pick is willing to switch with them. If you're going to do that just make sure you have a wide variety of champions to switch. If the enemy first pick gets them, then that rarely bothers me because there are only a few times this season where a champion has been totally out of control. If your main falls into that category, then I don't think it is unreasonable to expect a ban.