In the US, most chain hotels do check ID, which means they can check age. The hotels can refuse to check-in booked persons who aren't legally-required to be checked-in even on prepaid reservations.

Hotels in the US don't generally turn away guests who are 18-21 years of age when the guests show up with a bank card in their own name + passport or out-of-state driving license unless something else is going on.

In the EU/Schengen area, 18-21 years olds with their own bank card and passport shouldn't face the kind of problems with checking-in that happen in various places across the US.