I don’t know if I’d call it a Frankenstein monster, but I think it’s flawed.
1 - IMHO it might be OK if they knew ahead of time. I imagine most people expect an email to either go unanswered or to be answered via email. I also think most people expect that email will be relatively private and might be upset if the content was public.
2 - I’m not so sure Discourse would be the best choice for an “inbox”. Discourse is designed to be a discussion platform, not some sort of a “ticket system”.