The game has a built in adult language filter that you have to turn off to disable...
The mature language filter is simply there to prevent some players from dealing with communications which might offend their sensibilities (whether it's personal reasons, religious, whatever). Swearing, in general, is not punished, except in the cases of which it's used to attack someone.
...and players have the ability to hit tab and mute all or mute you and mute all chat.
And the mute feature is a short-term defense tool against toxicity, not an excuse to allow it. The burden should not be on players to have to mute you because you want to break the rules - it should be on you to follow the rules.
Chat violations outside of the specifics I mentioned should not result in you getting banned from playing.
Continually chat restricting someone doesn't work, though. If they can't be bothered to play by the rules - even despite several warnings that they need to change their behavior - then why let them play at all?
There's a certain point when it's clear that the punished player isn't going to reform, and that's the point where Riot has to put their foot down and ban them.
I feel like inting, griefing, afking, troll item selecting, deliberately ignoring the team and wandering around doing nothing deliberately should lead to bans because they ruin the game for all 9 other people...
Those offenses do lead to a ban. Intentionally feeding, griefing, trolling, and active non-participation results in a 14-day ban for the first offense, with a permanent ban as the second.
not chat violations, which do not ruin the game...
For you. Just because flaming and toxicity does not ruin the game for you, does not mean that it doesn't ruin it for anyone else.
I, for one, absolutely hate playing games where my team is flaming each other. It detracts from the game, and I may be able to mute the two flamers, but is that gonna stop them from dropping the game to keep at their flame war? No.
There is a reason Riot punishes flaming; whether you like it or not, and whether you agree with it or not, flaming and toxicity ruin the game.
...especially considering the players can control the chat they see.
Again, see above - both that the mute feature existing is not an excuse to allow toxicity, and that I may be able to mute flamers, but that's not going to stop them from flaming.