Where have you seen this? Maybe I haven't been in any rich peoples' houses, but I've never seen a house with any kid's bedroom having its own private bathroom.

I've seen it, although it depends on the surrounding demographics. The suburbs I currently live in, it's uncommon. But much of the newer urban housing I looked at before deciding on a place had that particular set up. As well as some older housing, which happened to be in the vicinity of a local college.

Barring the specifics of rich people's house, you'll generally see this set up in places where the "kid's rooms" are not, in fact, intended for kids. Where I've seen it in urban homes, it was designed so there was definitively a master suite, but then every other bedroom came paired with it's own en-suite. From my understanding talking to builders, it's done this way since a large chunk of owners in that area are young professionals that rely on renting out other rooms in the house (whether to other young professionals or AirBNB-style short term rentals) to afford the home. In college areas, you get similar rational, but because every room tends to be rented out to a student, there's usually not a definite "master suite" and all of them tend to be similarly sized and equipped with amenities.

While the bathroom may not be "private", I've seen loads of houses where there is a 1-1 ratio between bedrooms and bathrooms. Often times a bathroom for the kids room is accessible both from the bedroom and a hallway.

I've seen quite a few where 2 'kids' bedrooms have a "jack-and-jill" bathroom (eg, a bathroom between the two rooms, that connects them both).

Satisfies the "kids bathroom" and "sharing" all at once!