Actually, the useful part of the geostationary orbit is 1 dimensional, because the satellites have to be at the right height and over the equator. It's called the "Clarke Belt": https://en.wikipedia.org/wiki/Geostationary_orbit

But anyway space is very big and the probability of collisions is still low. Two geostationary satellites out of control would probably not collide, they will pass a few hundred of meters away in any direction. The big distance between them is mostly to avoid interference between the radio signals.