Why is it a waste of money? Having a hotel room for a few hours to freshen up or take a nap is a nice idea after a long flight.

Just tell the hotel your arrival time -- no need to lie. Some hotels, especially at the airport, have day rates, hourly rates, late check-ins, etc., so it might be worth asking about these options, as well as a late check-out so your friend gets the room for more than a couple of hours. Otherwise, this is a perfectly normal procedure.