In the UK, at least, it's unusual to show a driver's license for anything (except buying alcohol if you look young) because many drivers don't carry them, whereas in the US I had to show it every time I even checked into a hotel and even occasionally when buying things with a credit card.
Sometimes workers get tired of dealing with persistent people who absolutely insist that they are correct (which in this case they were), and realize that they don't get paid analyst wages, they get paid front desk wages, and they say "Okay, this looks right to me. Here you go."
No I don't mean all of that. He wrote "In Europe this would literally be zero problem, hence my attempt." I'm curious, if you can get a hotel room key in Europe without ID, how does that work? Does the phone work as proof?