"This house has a floor drain under the washing machine, with (as usual) the floor sloping towards the drain. Ditto for under the water heater."
...
"I have never, ever seen this feature in any other house, and it costs next to nothing."
...
I have some things to say about this ...
It seems like an obvious win to put a floor drain in places that could potentially flood - especially the laundry room, but also (why not) bathrooms ... wouldn't it be great if a toilet overflow or a bathtub backup, etc., could be confined to that space ?
It's a good idea, but there are some complications ...
First, if it's a real drain, plumbed to sewer, then you need to keep it regularly watered - as in, pour a cup of water into it every day or three - or you will get sewer gas intrusion into the house (potential life safety hazard). The water in the trap will evaporate since the drain is never used so you need to keep it full.
But if it's a real drain, the value has diminished since the backup might be below the drain and you flood anyway. So instead, you might consider draining to "daylight". This solves the trap/gas problem - you just drain to the outside. But, depending on your climate, this might be drafty - it is, after all, a 2" pipe.
Finally, to make this work, you need to slope your tile which is either impossible, since perhaps the room already exists and is already tiled or adds cost and complexity to the new construction that is unexpected because, as you say, typical bathrooms and laundry rooms don't have floor drains.
Here is how I solved this problem:
1. I tiled the bathrooms and laundry room with cove-base tile all the way around. These rooms are now 4" deep swimming pools. So I don't need any slope.
2. I installed a linear drain at the threshold of the room, right on the doorway line:
https://www.schluter.com/schluter-us/en_US/showers/shower_wi...
... usually you see these in showers, but it worked perfectly right at the door threshold, since you can cover the insert with the same tile that your floor is tiled with.
3. I didn't care about the draft or heat issues because I live in California. I simply capped the end of the pipe with screen for insects. However, if I lived in a different climate, or if I wanted to improve this design, I would consider placing a very sensitive (2-3 PSI) check valve at the end of the pipe. The drain would now be closed, but if the pipe fills with water (and you have 3-4 feet of elevation drop) then the check valve will open. More complexity, though ...
This has all panned out well. The only minor item is that there is a very small gap between the door trim and the start of the linear drain but with some very careful caulking you can sort of "dam" that tiny spot to ensure the water gets to it if its coming along the wall.