A quick Google tells me that there are 17,500 au pairs in the US in a given year. That's not a lot in the grand scheme of things but probably doesn't capture all live-in or otherwise more or less full-time child care arrangements. And of course, it's only an arrangement a couple will need for a bounded length of time.

It's not very common much less routine but if I heard a presumably well-paid tech person tell me they had an au pair or nanny, it wouldn't cause me to think "They must have family money" or anything like that.