I’m in the US and have worked as a nanny quite a bit over the past 20 years.
It’s the norm here for families with 2 high earning parents to have help, but an actual housekeeper would be quite unusual. I did know a couple of families who had this, but they were extremely rich, not just higher earning professionals.
For my typical families they’d have me for the kids, a cleaner every other week, a dog walker every day and a lawn service every week in the warm months.
Me (the nanny) only takes care of kid management. No cleaning other than messes we make together. But yes to kid laundry.
The cleaner does heavy cleaning such as floor washing and bathrooms and the kitchen. No ironing, laundry, groceries, changing beds etc.
And for whoever pointed out that these jobs can be great for working around your own kids, that’s exactly why I did it. And where I am, childcare would be around $25+ per hour. Cleaning is more, about $35+. So it’s worth the effort!
Now I just do part time with a 9 year old after school, so even though it’s not technically “my job” I always empty the dishwasher if it has been run, fold any laundry in baskets (but don’t put it away) and take the dog for a walk if he’s been cooped up in his crate. The 9 year old isn’t very needy and the parents appreciate any extra little thing that gets taken care of. They still have a cleaner and a gardener!
I agree with the OPs classification of housekeeper as a cleaner here wouldn’t do any of that extra stuff.