From what I've read recently, some
of the Maitre' D's are checking cards and not allowing people booked in Traditional Dining to eat in Anytime Dining. (It seems to depend on the Maitre' D.) There are usually so many people who want Traditional Dining that they're not letting people switch for a night or two.
As LisaK said, if you want to switch for the whole cruise you'll probably be fine since there will most likely be others who want Traditional Dining who will gladly take your place
Anytime Dining is one of the top reasons we book Princess. We love it!
Have a wonderful cruise!