Hmm, interesting idea. This seems similar to my thread here:
The consensus seems to be that someone who is assigned a task needs to speak up if they have concerns about the assignment or due date. Your suggestion would be helpful to take some of the intimidation away from this back-and-forth, especially for people who assign their superiors or less-close colleagues to tasks.
It seems straightforward enough to have a request become an In Box notification, but there might be a question about how to treat requests while they’re pending, and what happens if someone makes a differing unilateral assignment and then the request is accepted later.