Hey's screener feature shows there's a lot of room to innovate on giving users control of their attention beyond the filters and labels that Gmail has deemed sufficient for more than a decade now. Setting up forwarding to use Hey as a read client for my incoming gmail email has shown me that my address being old and public is not the problem.
Inbox had bundling that was a promising direction, but that seems to have been scrapped when they shut that client down. I'm not a tinfoil hat person and don't really mind being tracked, but it doesn't surprise me that a company that makes its living off monetizing attention would never lead on giving control of it back to users.