I've still yet to hear a solid argument against this simple suggestion;

Just make using chat a privilege that can be taken away.

Done. Toxic people get muted. Three strikes and muted for life. People who aren't dicks about it get to keep chat and presumably be helpful to their teammates. Bonus point; Since being a dick can result in losing access to chat, maybe people will be think twice before being a dick in chat, "I've been muted for 24 hours, maybe I'll curb my toxicity a bit", wishful thinking? Probably... Christ, this is the exact same system they use on these forums, which I'm likely about to incur for repeated use of the word "dick".