I agree, from a usability standpoint, that your suggestion makes perfect sense.
I will, however contrast it from a system pont of view.* If you make it easy for the user to never have to go into their mailbox, they're less likely to go in there and clean things up.
I'm not going to pretend that I know what the correct balance is between the two (or even if the issue w/ not cleaning up is significant), but I've seen systems where a few people never weed their messages, and they might collect up thousands.
* (I don't know anything about this system, but I have administered mail systems and portal sites in the past)