I have always wanted something like this without having to move away from Git (to Fossil).

A bug tracker like this allows the bug history to be tracked and remain with the source code which is much better than keeping the bugs in a web based service because every 5 years you need to migrate it (Bugzilla to Trac to JIRA) and in every migration, some context or formatting is lost.

For something like this to be successful in enterprises, the tool should be management-friendly. Right now JIRA leads because it allows management to pull pretty reports out of it. Is there anything planned in git-bug to appease these management type people so that it has a good chance of taking off in the enterprise world too?

Upvoted for Fossil reference.

Now we just need to be able to also put a wiki in the same repo.

I do this with vimwiki: https://github.com/vimwiki/vimwiki