This proposal is very similar to the abuse of the notification bar. Take a look at this screenshot:
Three notifications! None of these are important (*):
- +100 Reputation.
- Associated accounts.
- Privileges gained.
As you can see, the notification bars are on top of the page, preventing users to access the functionality at the top of the page.
I propose all notifications get classified according to importance and less important messages could be put in the inbox.
(*) important enough to justify the disrupting the concentration of people.