Just a suggestion Riot before you read this put yourself into my shoes.
Chat banned people should have the power to /all chat. I don't know why Riot disable it.. tbh http://boards.na.leagueoflegends.com/en/c/miscellaneous/omRwQOUA-last-message-to-everyone-and-riot-actually-read-and-comment-please?comment=000100000000 I have a story why we should have the privilege to /all chat right up there ^
And if you were never chat banned you have 3/5 chats. And after you use all 3 you need to wait 5 minutes for another chat (1 chat). Depending what you were chat banned for verbal abuse/offensive language/negative att. You should either have more chats available when you first start or less time to wait for another chat.
When you first start a game any mode. You have to say a lot of things as a different role if you wanna communicate and win. Such as "I'm a little rusty as this _____, so ganks appreciated please", "Next blue please/ward buff please", or even please ward that place or something like where is _____?" It's hard to win if you can't communicate.
First off, I think chat bans are stupid. Just mute them if they are being dick heads or hide chat. Simple. Sometime people are trying to become a better player then before when they were being toxic but with these they can't communicate. Other games have mics and its worse then just seeing words on the left corner. But you can't get chat banned. You simply just mute them.