Didn't say that snow/lawn work was $10k/year, I indicated that was in addition to (more expensive, typically) housekeeping services.

My point was that Americans very much hire household assistants, but they're specialized and on-premises for a short time to maximize value and minimize costs. In the past week, I've had housekeepers, lawn service, a plumber and a handyman at my house. They were all great, and did better work than I would do, but I wouldn't have any of those people do the jobs of any of the others. Why pay $20k to a generalist 10 hours a week when I can get specialists who can do more in less time?

There just isn't a great need for non-specialized assistance at $20k/year. My housekeepers and lawn service are on auto-schedule and auto-pay, so they require a bare minimum of my time. I would have a hard time trusting a low-paid part-time personal assistant to facilitate and review plumbing and construction work beyond the most basic fixes.

Think about a single renter with a small to medium size apartment. They don't need groundswork or maintenance, that's included in the rent. How much housekeeping do they need in a small to mid-size apartment? They often get grocery/food delivery and/or just microwave stuff. There are plenty of delivery laundry services or apartments with washer/dryers en suite. How many errands do they need to run that they don't need to be personally present for? You can't send an assistant to the DMV, after all.

Think about dual high earners with kids. They're going to need child care, and that's going to take a huge bite of their income. They don't need a 10-hour-a-week assistant, they either need more than that at home (a nanny), or they're white-knuckling it to save for their kids' current or future school tuition.

Think about a single-earner couple. One of the couple can stay home and take care of the kids and all of the things that an assistant could do.

tl;dr: Americans absolutely hire human assistants, just not in the kind of generalist model you're thinking, because it's just not worth the kind of money it would take.