I have. UMich has been saying it for years.
https://admissions.umich.edu/apply/freshmen-applicants/requirements-deadlines
The issue being that some colleges want to receive everything electronically and rushed scores, at least in the past, were always paper.
But for the OP, AFAIK Arizona does not prohibit rushed scores.
In general, rushing saves little/no time, so is a waste of money. Also, in general, if a college prohibits something, it will say so, and not make you guess.