Honor system should take a players Honor into consideration before applying restrictions.
I recently received a 10 game chat restriction that came with Honor rewards being taken away. I really value good teamwork, one of the reasons I enjoy playing League so much. In the 2 games I was reported in the arguments started from my teammates being toxic by saying someone was "inting" when whoever died just made a simple mistake or saying that they purposely don't want to help the team. It can be very frustrating and somewhat tilting to see teammates talk like that, so I took it upon myself to let said teammates know they were being toxic and ruining the game for others. They apparently reported me and the system picked up my logs as being "negative".
It was very disappointing to have Honor rewards stripped when I have otherwise been a very honorable player throughout my years of playing League, I even have the Santa Baron icon for what it's worth. My point being, if a player like me has years of a honorable record but happens to get caught by the system when he was having a bad day for two games, that doesn't sound like a Honor system that rewards good behavior, but rather punishes those it catches without any consideration of their Honor.
My suggestions would be maybe something like a warning for high Honor players when they misbehave and get caught by the system. Or maybe just a 1 Honor level drop for people with higher Honor or a good history rather than an immediate drop to Honor level 0.
Edit;
I feel like some people missed my point in wanting to talk about the Honor system and not so much my specific situation, I was just providing some context.
Also not a great first experience on the boards to have my post downvoted out of visibility. I originally had a discussion with Player Support about this topic. I was told they can only provide context and not push my feedback anywhere but they pointed me towards the boards here if I was looking to have my feedback be seen and start a conversation.