I've stayed at a hotel in UAE that took a deposit that they returned on check out. They were perfectly fine with it in cash.
Last time I visited the US was in 2016 and back then my country wasn't an international outcast so I had a debit card that counted as credit in the system. I'm just curious what people like me would do these days. Or maybe the hotels I stayed at were too cheap.
Possibly you can also put down the same amount they take as a hold on the card in cash, but I've never tried it.