One reason I can think of - in some places where houses are small (like in cities the UK) you might not have a garage on your property and might rent one nearby (they are often in little rows, e.g. [1]). So they might have that kind of situation and have the washing machine there if it's a very small house?
It's tough times: their villa has a washing room in the servants block away from the house, but now they had to release everyone but the valet, housekeeping, masseur and hairdresser, so the washer role has been eliminated and now they need the notification for their valet to go pick it up.
Correct. Have several houses on the land, and it made more sense to put the machine where it was both equidistant between them and where the washing line is.
No, the obvious over engineered solution would be to mount the machines on a train (or tracked vehicle for bonus points) that can come when called and go where needed!
The problem (scratch that, "the most interesting challenge") with that is that a washer needs a water supply line, water release outlet (if not for chemicals, might not be the issue on a farm) and electricity (perhaps a simple problem to get power connections to it through the rail like trains).
Nah, you just put a 5-10kwh battery on there, along with a small water tank and pump - a load of washing (in Europe) only uses 50L and about 2kwh tops - up to 5 with drying. The rest of the battery powers the drive train for the vehicle. Then you just have a dock for charging and water replenishment. We only use zero phosphate eco detergent, so waste can be dumped wherever. Maybe position it to water some plants when it drains.
You know, my whole life is madcap projects (today is running half a km of fibre down the inside of a live water main) so I’ll update you when I have a mobile laundromat.
1. https://www.alamy.com/stock-photo-row-of-private-car-garages...