Honestly I see no reason at all that this outweighs the consequences. Over the course of the months, I've had numerous reports that I misinterpreted or didn't really do fully because of hastiness. Also, sometimes server issues can mean that a thread/post wasn't closed/deleted like requested. I'm always really grateful for somebody to read through their report and mention that I didn't do it correctly.
On the other hand, I doubt hardly anybody uses the New Posts feature. IMO, the only reason people go is if they want to farm post count... You're asking to sacrifice something that has a lot of usefulness for something that is only to get people's e-pen larger.
The suggestion about being archived after an hour or two is, I think, too much to have to mess with.