A day rate is generally nothing to be ashamed about asking for, especially at a hotel near an airport or railway station. A manager with an eye on revenue management can make a bit extra renting out a room during the period between an early check out and a late check in. Sometimes there is a condition not to get into the beds in order to avoid a sheet change. I've seen 24 hour rates in some places, check out the following day at the same time as you checked in.
Hotels offering an hourly rate are usually a different matter however.