Rumors of any hotel room shortage are unfounded afaik from a recent trip. You will not be forced to sleep on the street. LOL However, star rating may be an issue. Some properties, hotels, but especially those less expensive rooms in private homes (casas particulares) which allow the visitor to have an excellent experience with Cuban people, may not be quite up to the standards of some first world visitors, mostly due to shortages of certain construction materials. If you wish to be insulated from any and all discomfort on a ship or at a 5* property or within the confines of a resort, and being hauled around to sights in a large air-conditioned bus full of other foreigners, you will pay a premium, and you will also IMO lose a good deal of the flavor of the country and its warm-hearted people.
There is currently NO real reason to have fears about "being on the wrong side of US policy" by traveling. Applying for a pink "tourist card (visa), you simply check a box indicating the reason for your trip; while tourism is still not one of them, there are cultural activities reasons as well which fit with the interests of most travelers. NO ONE (US government) is checking or has been for quite some time, or asking for any proof at any time after the trip. On return, at Miami airport, the immigration officer merely asked where I'd been, how much rum and how many cigars I was bringing back, and wished me a welcome home.
It's a wonderful country with wonderful people, and I hope you decide to visit.