I do it when I have the incentive liek such a promo now. I have an upcoming trip to London next week, and changed my 4-night stay at Hotel 1 to following pattern: Hotel 2 - Hotel 1 - Hotel 3 - Hotel 1.

I was thinking yesterday that in big cities with many propreties they could have a sepparate rate "hotel-hopper". It could be more expensive than a regular rate, but in the end give you the expected benefits. This would be cheaper for the hotel (lower running costs), but would generate a lot of discussion around the T&C.