My present house (in Ohio) also has its singular bathroom upstairs. The bathroom is on top of the kitchen. Neither room is an addition -- as far as I can tell, it has always used this basic layout.

According to aerial photos, it was built in the 1950s. It resides within a small but very industrialized city that was positively booming at the time the home was constructed; it definitely included plumbing from the beginning.

A previous house in the same city was definitely built before indoor plumbing. It was even built before separate kitchens were considered normal or necessary. It originally had only two rooms downstairs, and two rooms upstairs. Heating and cooking would have been provided by a central stove (probably wood-fired, and with no ductwork).

While it was stick-built, it was initially only a step or two above a fairly primitive log cabin in function.

By the time I lived there, it also had a kitchen, laundry, downstairs bathroom, another upstairs bedroom, and subgrade basement added. The bathroom was part of the kitchen addition, and one entered the bathroom through the kitchen.

I've actually lived in three houses so far that were initially constructed like that -- with two rooms downstairs, and two upstairs.

Only one of those 3 had a bathroom that was separated from the kitchen by a room, and that one was perhaps the oldest: The floor joists for the first level were made from logs that were hewn flat[ish] on the top by hand, and that still hard bark on them. For that house, the bathroom was its own small separate single-story addition that jutted off of the side of [what had become] the dining room.

The house I grew up in was larger and much more-nicely finished in terms of things like woodworking and trim, but was also very old by US norms. It was built before both plumbing and electricity, though it included gas lighting (!) in every room. The partial basement, kitchen and downstairs bathroom were additions, but the bathroom connected to two different common rooms even though it was physically adjacent to the kitchen. There also was an upstairs bathroom, and which was created by taking part of the master bedroom and making it into a hallway while the the original bedroom closet became the bathroom (with a small and somewhat haphazard roof extension where the bathtub was).

Anyway: The point, other than that old houses present interesting evolutions, is that old houses often (but not always) had bathrooms attached to the kitchen -- and that we usually seek to keep them separated these days in newer construction, at least in the US.

I've also lived in a few different apartment buildings (many of which were "old", but all of which were initially intended to be apartment buildings), and all of those bathrooms were separated from the kitchen by a hallway.

And all of these bathrooms had doors. I don't understand the questioning of bathroom doors that I see here in some comments -- at all.

(I shall spare at this time the details of the house I once owned that had been an old farmhouse (with no gas, no lights, and no plumbing), and which had subsequently been divided into a triplex that contained a total of 17 distinct rooms. I could probably write a whole book about that place.)