I don't think I've ever not been asked for my passport (or some other form of government ID) when staying in hotels in the EU. Two weeks ago I stayed at a large chain and I was asked for passports of my whole family.
Been a while since I stayed in the EU, but I was in Brussels in October 2019 and stayed at an Aloft at the time of an EU summit. I distinctly remember remonstrating with the clerk about the embarrassment of my British passport when I handed it over.
