I'm getting real tired of noticing new answers or comments to my questions hours after they were posted because I minimize StackOverflow and resumed working. According to this question's answers you're never going to implement instant email notifications, so could you at least give me a sound notification or desktop notification when new inbox items appear? You can even make it optional! Everybody wins.
This would literally just take a few minutes of coding to implement. You already have the events in place, and you've already set up desktop notifications for chat. Come to think of it, I could probably write a Tampermonkey script for this.
My point still stands though. Please consider this.