While I can understand the rationale behind channel chat and whispers being treated separately, the fact is that users who are banned for inappropriate behavior often follow up by harassing the streamer directly through whispers. Here is a potential workflow I can think of:

Whenever a mod bans a user from a streamer’s channel, it triggers some kind of message/notification to the streamer that a user has been banned and asks if the streamer would also like to block/ignore. Additionally, there can be an option for the streamer to auto-block in these instances where mods are trusted and there may be too many bans to manage.