Rivers clearly demark the boundary for anyone without GPS or other means of determining a precise location. Same as hills and mountain ranges, which are also common boundaries.
The fact that some rivers can wander and people tend to bold cities across rivers is a thing against them, but people build across any kind of boundary.
Rivers are natural points for cities, almost every city not on the coast is on the river because that’s how it was originally settled. So to have half the city in one state and the other half of the city in the other state is absurd. People build across anything but again cities are naturally on rivers.
Economically the immediate area on both sides of a river are going to be similar, so you should have the same administration. It’s when you get away from the river that this changes and you might want different administration.
Of course a settlement wouldn’t be split by the river, instead the border would shift according to the settlement’s boundary (city wall or such). Easy way to encroach on others territory, and the perfect place for demanding wayfare/toll.
Borders along rivers make no sense, fight me.
Borders don’t make sense

Rivers clearly demark the boundary for anyone without GPS or other means of determining a precise location. Same as hills and mountain ranges, which are also common boundaries.
The fact that some rivers can wander and people tend to bold cities across rivers is a thing against them, but people build across any kind of boundary.
Rivers are natural points for cities, almost every city not on the coast is on the river because that’s how it was originally settled. So to have half the city in one state and the other half of the city in the other state is absurd. People build across anything but again cities are naturally on rivers.
Economically the immediate area on both sides of a river are going to be similar, so you should have the same administration. It’s when you get away from the river that this changes and you might want different administration.
Of course a settlement wouldn’t be split by the river, instead the border would shift according to the settlement’s boundary (city wall or such). Easy way to encroach on others territory, and the perfect place for demanding wayfare/toll.