Firstly Tyler1 was a semi-prominent streamer. He had a decent following and was essentially showcasing and promoting the league experience for everyone to watch.
Secondly he would consistently troll, int, and rage in chat. Doing it in a way that was humorous and thus in a way encouraging similar behaviours from players watching him.
Thirdly I am willing to bet that he has the most Perma-Banned accounts of any other known player. He consistently created negative environments for others to play in and prove that he would never change his behavior.
Under normal circumstances he probably would have remained banned and able to make new accounts and stream his matches. But he was clearly abusing the system for his own profit and giving Riot a bad name while doing it. He was starting to get more popular which created a dangerous scenario where he was influencing a larger base of other players and making them think it was okay or funny to ignore the rules and harass and troll teammates. This was on a scale that was far and beyond a normal player.
That is why Riot has a ban on sight policy regarding Tyler1. He had more then enough chances, and he can still play as long as riot doesn't know its him. But he will no longer be able to make a reliable profit from showcasing Lol games.