The LP loss is a bit much, but an anonymous vote to kick similar to what WoW has for it's LFG system would be extremely helpful. The way it works is that all players get to set up a vote to kick and depending on how often the player uses it the CD on it will be longer or shorter (longer if you're trigger happy with it). then everyone but the player is given a chance to say yes to kick, or no he's fine. After that the group goes back in the que to find another player.
Although a huge improvement to this would to be to make it a majority vote, that way duo's can't que up and protect themselves from the 4 vote so they can troll. Also instead of prompting other players to decide, you can simply click vote to kick on the side of their nameplate if you feel like a person is exibiting Toxic behavior. Once three votes are in the player will be kicked and the group reque's.
This helps solve a lot of issues duo que has, while it does help to have someone you can communicate with, often times Duo's tend to que together to block off different roles, or to protect themselves when they want to be toxic. So the 3 votes mean no Duo is safe from being kicked despite wanting to exibit toxic behavior, It prevents ganging up on a player with the vote to kick feature (you would still require a third vote from another player to kick even if you're voting together). Even if a player is being bullied by a duo, the third player has to be contacted so there is a record of it if it's through the client and therefore can be tracked in terms of abusive behavior.
It's not foolproof, but it will help make the game itself a lot less toxic. Course this can't be implemented in the normal que feature as it's easily abused, but it's a much better system than telling your players, deal with it and then use the report system to help us find them later for a temp/perm ban. Also if a Player gets kicked often it becomes very apparent that there is an exibited behavior that the community does not approve of.