Riot already cracks down on flaming and trolling, both by administering escalating penalties for infractions AND restricting access to honor rewards for punished players. There are consistency issues with the actual implementation of these penalties, but the framework exists. Ultimately, you can't fix stupid people who have no idea how to conduct themselves in public and are ignorant of the cost of failing to change, which describes most banned individuals.
I don't think 18+ fixes this. Plenty of adults are idiots. Plenty of kids are respectful.
Honestly, the best thing Riot could do for the community is to adjust their F2P model, requiring an investment of something like $10-20 whenever a new account is created, to be paid back doubly or triply in RP. This would actually cause accounts to be something that the individuals are interested in protecting, and would force assholes to reconsider their conduct. But it'll never happen, because it would thoroughly fuck up Riot's bottom line.
Idiots being idiots is a reality of any online game, especially a free-to-play game. I don't think an age restriction changes that.