In the USA, you could just leave without telling the front desk that you're checking out. You'd be automatically checked out the next day and get the bill by email. In many foreign countries this dcoesn't work, although you might be able to ask a willing front desk agent to check you out after midnight or to change the time on your bill.

IMO if you paid an overnight rate and arrived at the hotel, you should get the (first) night (and stay) credit. Otherwise it can put the customer into a position of arriving before midnight but losing out if there's a line to check in, for example. It would be different if someone would show up for a few minutes to check in, immediately leave (which some folks here seem to do on USA mattress runs), and then expect credit for the next three weeks at a cheap rate.