Many streamers have the same problem where someone is abusive in the chat. In this case, they are banned. It is more than common that the same user would come back on an alt to continue being abusive in chat.

My suggestion is to notify broadcasters/chat moderators of accounts that are on the same IP as someone who has been banned or timed out, so that they could deal with them accordingly. This could even be extended to allowing broadcasters to IP ban people from their chat.

Yes, there may be a problem with people using VPN's, however this is generally the minority, and the implementation of this idea could dramatically reduce the amount of abuse towards broadcasters.