I regularly keep my user talk page having unread messages, because the orange bar makes me not to forget about tasks. But AWB pops up the New messages panel and doesn’t let me edit until I read the message. (And there is not even a close button on it, I can get rid of it only by pressing Alt+F4.) I think users are not idiots, they can decide on their own whether they want to read that message in a way that MediaWiki knows they have read it or not.
I strongly disagree with implementing this. It's an extremely bad idea to let new messages not interrupt runs. Bots depend on this behaviour, as do users in need of a trout, or users that are making a mistake without knowing they're making one.
Do not implement.
I’m OK with a notification that pops up when a new message arrives so that I know something important happened. But I’m a mature human, I can make a decision on my own, especially as having an unread message indicates in no way that I don’t know what’s in it—I may have read in the notification email, by hovering NavPopups over my user talk link, the sender may have reported the same on IRC noting that they wrote on my talk page too, etc. There can be a huge warning message that how bad guy I am if I don’t read the message, but please add just a tiny button to keep editing. And it’s nonsense that I can’t even exit without reading the message immediately.