If upper floors' floor drains route to lower floors before joining with other plumbing on the lower floor, that would prevent backups from rising to the upper floor drains (unless their particular pipe was clogged, which should be unusual in a residential floor drain). But you'll have this issue at least at the lowest level of the dwelling.
Basements are not common where I've lived, but where present in custom houses, they tend to be fully finished and plumbed and then they'd have floor drains too.
In some buildings elsewhere, I have seen a less finished basement, with only laundry and a slop sink... That slop sink may be where a backup from the lateral to the utility sewer (or septic system) would come out. But that's not a common look for a fully custom home.
Lived in an apartment where the front-loader managed to pump a sock into the high-flow drain where it got stuck. That was fun...
(Also had a front-loader break it's door seal, also a lot of fun...)
The washing machine, not so much. The water lines and spin cycle aren’t particularly loud, but they’re loud and distinct enough that it’s too loud for me at night.
I'd love to have an upstairs W&D, but I wouldn't install one with a secondary drain pan.
Some reasons I would not want this is: need to pour water in periodically to keep the trap from drying out and the risk of a sewage backup covering every room in literal shit.
It is really weird that for all the smart crap manufactures want to stuff into appliances, leak detection isn't particularly high up on the list. It can't really be because it's hard to do, leak detectors are often one of the earliest sensor types available for new smart home kits.