I moved to Belgium where apparently it's also normal to put toilets in the bathroom, and I still don't understand why one would put the dirtiest place in a house in the same room as the cleanest place.

I don't want to shower and brush my teeth just a meter away from the toilets.

In the US, a "bathroom" is usually a 3-piece (bath/shower, sink, toilet). A toilet/sink (no bath) is usually called a "half bath" in real estate listings (2.5 baths is common in suburban homes - one master suite, one serving the other bedrooms, and the "half" near the kitchen or living area).