I believe there is an age-out age for being an au-pair, 26 I think, so it isn't possible to make a career out of it.

I'm talking about the "the host offers a roof, pays next to nothing for a live-in nanny" arrangement, which locals don't do.

Interestingly the 26 refers to the USA. But a similar career would be legally possible inside the USA (not under the program) but not in EU, due to heavy labour regulations.