Not quite the same but near some universities in Bangkok, some shops have opened renting cots by the hour, for students to take a nap.
Don’t they have libraries for that?
Seriously, I used to know where good napping spots were in the University libraries.
I have seen day use fees for hiker hostels, where you can stay for a few hours, do laundry, shower etc but not intend to stay for the night. For long distance hiking, if one arrives too early to stop for the day, but could use some services it is not uncommon. Sometimes those fees are just shower/towel and/or laundry, but not uncommon for the hiker to find a place to relax and lay down a bit. Now those are hostels, which usually are bunks and comfy couches in a separate area. Such a person would be more likely to use the comfy couch or a outdoor lounge chair then a bunk during that time.
Sometimes all the good spots are taken. Often commuter students will crash for a few hours in a friend’s on-campus housing. Rent-a-cots would probably be used likewise.
This. After a long race/ride/athletic event a shower & a quick nap before heading home would be WONDERFUL!
I did a race in Salt Lake City, got a late checkout (1pm) so I could shower/change but then where do I hangout before it’s time to head to the airport for my redeye home that evening? I’ve also done 24-hr races, morning to morning. I’m not safe to drive home at that point, I need some sleep (& a shower); a couple of hours in a hotel to rest up before the ride home would be just what I needed.
The only legitimate ones that I’ve heard of, & would use, are at airports. Anywhere else, I’d spend longer disinfecting the place that I’d plan on staying there. Never heard of one for the driver who needs a break from the road (except maybe a truck stop), or someone in the downtown area of the city.
I once rented a room for two hours to watch a Formula One race. I was visiting someone who didn’t have cable, and I’ve rarely missed a race in the last 40 years.
I’ve seen downtown hotels renting day rooms for a corporate interview day or state licensing exams.
Looks like “the underground hiding place of the yote”. 
I guess the yote is kind of the head honcho. I’ve always heard of his subordinate, the coyote. 
I know you wrote “per-hour” but I once stayed at a hotel in Atlantic City which charged $20 for one day, and $40 for one hour! True story.
I’m the same age and it used to be very common. Since I have been interviewed in a hotel room, and seen many examples on TV of people being interviewed by journalists in their hotel room, and many of my friends at university were interviewed by international companies in the hotel rooms of the airport hotel, I’d be less likely to laugh than you are.
I understand that now it is more common for hotels in that business to have rooms without beds to rent out for that purpose, but back in the day we didn’t use to be so precious about private space.
Back in the day that the Montrealer ran between Washington, DC and Montreal, one of the cabin attendants told me that they would typically arrive in Montreal around 9 or 10 AM and go out around 5 PM. Amtrak rented them rooms in the Queen Elizabeth Hotel (built on top of the train station) for them to rest, shower, etc. Their “day’s” work consisted of two 20 hour trips with this 7 hour break in between. But that 40 hours was a week’s work and left her the rest of the week free. She was an aspiring writer.
A number of larger airports have “mini-suites” that you can rent by the hour. They have a place you can nap, showers, etc. I think some people use them just to have a quiet place to do a little work during a layover. They could be nice if you have a long layover between two long flights.
When I was a Civil War reenactor, my hot, sweaty friends in blue wool and I would rent a local hotel room at the end of the weekend for as short a time as possible, just so we could all shower and change into modern clothes before making our long drive north to home.
We’ve used the hotel in the Orlando airport exactly as described.
You get off the cruise ship by seven and are at the airport by nine - easy. You are told not to book a flight home until noon (IIRC), just in case. Flights that involve switching planes in Atlanta with kids SUCK, so booking a direct flight is preferable. They leave in the morning, and then at 4:00 in the afternoon, and then again in the evening…so you are going to be spending about eight hours in the airport with squirmy children. The Hyatt even has a pool. It doesn’t matter if its cheaper, that’s the way the flights home work for us.
I coordinated an event where the hotel even moved beds out of the hotel rooms and replaced them with tables for us to use in this fashion. But it sure wasn’t hourly - it was a weekend thing and it cost a lot to get a bed out of a hotel room for four days.