I disagree with this. When I was a poor grad student, laundry was the greatest time sink of my life. I spent many Sundays trucking loads of laundry between my apartment and my laundromat a mile away. $20 was definitely a reasonable sum to have that time given back to me. And I'm sure many of the other people I met there (often mothers who were disciplining unruly children) would have said the same thing. If you think this is purely an entitled tech worker problem, you've never spent significant amounts of time in run-down laundromats.
You don't need to install them; portable washing machines just need to be plugged into a faucet and a wall socket. They take small loads, but it's plenty for a single person.
Do you have a particular model on Amazon that you can recommend? I always thought that the only kind of washing machine is the big $600 kind that my parents had.