If your bug request came wrapped in some metadata about how it's a bug request, then it would be easy to further integrate that into all sorts of things.
OK, that's great. So why doesn't that happen? Because defining such metadata formats is a non-trivial exercise, and even more difficult is getting everyone to use those formats. So it turns out this is really just another specific instance of the Great Semantic Divide, namely, how the heck can we actually share semantics in any reasonable manner on large scales? It's the exact same reason the Semantic Web hasn't happened.
Further, even if that hurdle were to be crossed, you'd have the problem that somebody, somewhere has to fill out the definition of a "bug report" before it can be wrapped in the relevant metadata. Right now this step occurs when you take the email and translate it into your todo system (or bug tracker or whatever). In this perfect world this supposedly is done by the sender... but that, too, is fraught with problems, because that takes a certain level of skill on the sender side and now you've lost the aspect of email where you just click "New Email", bash on the keyboard for a bit, and hit "Send", and it mostly works. There's also some important context issues, which is that even if the bug or task was perfectly filled out by the sender from their point of view you'll still need to tweak it because you have a different perspective on things. (Which is just the Great Semantic Divide popping up again.)
In summation, you're not just screwed, you're comprehensively screwed.