I'll leave Matt to respond to the main request, but as a note:
It would be much easier if you supported a generic email in notifications
This is something we're discussing. Biggest issue is abuse (you'd be amazed, we even get spammers automating our 'invite a team member' just to inject a message as the name of the user being invited...).
So being mindful of how we open up the system to allow arbitrary emails, BUT, don't end up getting ourselves blacklisted everywhere for spam (which of course also costs us money to send).
Implementing a basic 'any email address would be fine' is relatively easy, ensuring that it works for everyone, but not abusers, is where there is some complexity :-) It's not a 'no', just wanted to provide some context on our internal discussions about this :-)
I hope that helps, and I'll leave you with Matt about the overall improvements we can make with PagerDuty.