I expect that quite a few hotel clerks in the US are just not familiar with anything other than a driver's license as government ID (or think a driver's license is the only acceptable ID). I'm pretty sure that I would have an issue with a global entry card at some point if I were to routinely use it outside of TSA (as I do after my driver's license issue) even though it's perfectly valid US government ID.

Generally speaking, hotels in the US do seem to want government ID. Don't really know the requirement in general. This was a fairly low-rent chain that I was only using because last minute. I expect if it had been one of my major loyalty chains, a manager would have fixed things pretty quickly.

ADDED: Normally I travel with a passport as well but, as I say, this was a last moment short trip so I didn't throw in all my travel pouches.