See, Riot isn't under any obligation to take ultimatums from you. They don't need to change their system, it clearly worked on you.
You admit to flaming. You claim you were "triggered" to flame by others in the game. The only thing you are permitted to type in retaliation to someone flaming is "/mute @champname". You cannot flame back, you cannot ask them to stop flaming.
You were banned because, probably, you did not heed the warnings of your chat restrictions you got before this. This is your final chance. The next time you are punished will be a permanent ban.
Game chat is for communicating about the game. Nothing else.