This bug annoys me alot.
This is a bug that needs to be fixed.
I wouldn't consider it to be the bug; the top bar is cached on non-SE 2.0 sites, which are the chat system and Area 51. The rep or achievements and inbox messages you've already read come away in a few minutes, for me in two, and doesn't really annoy me.
So, unless the chat system becomes a full-featured SE 2.0 site, which is technically not possible, this bug has almost zero chances to be fixed.