Then the issue comes down into an issue of "what issues ruin the experience the most?"
Put bluntly, your chance of getting your role is exponentially higher in the Team Builder setup. Sure, you're going to get the shitstains who queue for a role only to try to force someone out of the role they really want, but that should just be a highly penalized offense and your problem is resolved.
Before, you have brought up the issue of someone getting their champion banned and "being unable to play anything else", and frankly that's already something that happens.
Nobody is going to be at the same level with all roles and a multitude of champions. That's simply unrealistic, and isn't a measure of the player's skill. Sure, you can argue that the point of solo queue is to measure your own adaptability, but that's an opinion: I say it's about measuring a player's skill, and frankly there's a difference between skill and experience. If being mediocre at a bunch of different roles was really the display of a player's skill then the top players would not be exceptional at 1 or 2 roles and lackluster at the other 3 (compared to the first 2).
The point I'm making here is that your defense for the current system seems to come down to either an unwillingness for change or a defeatist/pessimistic attitude. Yes, there would be issues with a Team Builder system. Of course there would, as there are with any system. Saying it'd have "just as many" as the current system is decidedly proven to be false due to both systems already existing alongside each other in the non-ranked environment. Furthermore, the per-game experience gains from moving to a structure where the majority of your games you receive your best or most preferred role vastly outweigh the current almost-guranteed-fight-in-champ-select system that exists now.
Of course shitheads are going to be shitheads, THEY'RE the problem, not the system in place. The difference is, if you have the option to pre-choose your lane/role, not only do you have less shitheads acting like shitheads in the pregame ("mid or feed") because they're at least getting their preferred role, you also have a minimalized amount of losses due to multiple players being forced into roles they're not optimal in. Games should be decided by the skill of the players in game, using the playstyle they enjoy and are good at, not by "how well can they play a role/champion they hate to play", which whether you're aware of it or not is what you're advocating.
Being able to play multiple roles and characters should be a necessary part of game mastery, but needing to be good at roles you hate just because getting the roles you like is purely a matter of luck should not be embraced and should've had at least some steps taken against it by now. The point isn't that a Team Builder ranked queue would magically fix all the issues, the point is that it would fix one, major, game-defining issue that is hated by literally the entire community as far as I can guess: The problem that getting to play the role you like to play is left entirely to chance in ranked. This is a problem that has caused more friction amongst teams (at least in my experience) than any, and I mean any other issue by a landslide: Some guy is forced to play a role he sucks at or hates.
You aren't going to get rid of trolls. You aren't going to get rid of people who don't prepare to play other roles or champions. You just aren't. People are selfish fuckheads who suck at this game. The best course of action is to minimalize the amount of times those people are put into situations they don't want to be in, and a Team Builder queue alleviates that considerably whereas the current system does not. Ideally people would work together to build a team, follow pick order, and be competent at all roles before playing ranked. Until Riot puts HEAVY restrictions on those who do not (which they should've done ages ago), that simply will. not. happen. The most you can do is negate as many of the situations where it'd become a problem as you possibly can. Team Builder does this. Current queue does not.
The compromise might be that players are forced to queue for 2, with an optional 3rd, roles at once. Learning 2 roles to equal levels of mastery is a fair requirement for ranked. Forcing a player to learn 5 to climb the ladder is not. This would fix both sides in a few ways. Firstly, it'd lessen queue times considerably. Secondly, it'd force players to learn to play multiple champions across multiple roles to a proficient level, without forcing them to occasionally play a role they outright hate. Thirdly, it allows for team alteration in champ select without forcing players out of roles.