That is a good idea @eviltrout can you take that change for Monday?
Edit: errr, wait. This would mean unlimited griefing messages by new users against staff in private messages. No, that is not a good idea. Just increase your daily new user post limit in site settings if you run into this. The only sane way to do this would be to allow new users 1 reply (maximum) for each message they get from staff, which is too complex.