Webmail can do JS. Clients using full HTML engines like MSHTML, Gecko or Webkit shouldn't have an issue either. Text-based clients are the obvious exception, and they should still be rendering the same plaintext mail they've always been rendering.
Clients can also not implement AMP for e-mail, which I imagine is going to be the case for plenty of them.
>For what benefit to users?
Better interactivity in e-mails. Replying to e-mails is notoriously tricky to get right and often confusing, due to interactions with email threads, CC/BCC, address spoofing, etc. Interactivity via hyperlinks is acceptable but not ideal, especially for services that are actually performing operations on a GET request, which I'd argue is unwise. But also, hyperlinks in e-mails often contain sensitive tokens, which are easy to accidentally forward.
AMP interactions should be free of unrelated junk that e-mail replies would contain and can offer more functions. As for security, at the very least, Gmail strips off AMP during forwarding, which should make it safer to include tokens for interacting with e-mails in AMP payloads. Obviously that does no good for purely sensitive mail like password reset, but it's still an improvement.
>At what cost to users?
HTML and plaintext e-mail should continue to function for the foreseeable future.