As I understand seasonality – and someone here on the board posted a very enlightening article about it – it’s not that a virus goes away and returns but rather that it thrives in a certain sort of climatic window, so to speak. So, maybe those three states you mention would have had much worse spikes if they had happened in the spring or winter? Who knows.
As far as cases rising and falling in tune with mitigation measures, my take is that we probably can’t definitively say one way or another. There seem to be so many factors, all intertwined and all hopelessly confounding any analysis we’d like to make for any one of them in specific.
But having said that, Florida does seem to have mostly avoided the nightmare scenarios that some predicted when they decided to remove most restrictions. Texas and Arizona I’m not so sure about.