The problem is we want a lot of things to be in geostationary orbit, which is only possible at a specific altitude. That effectively transforms the "space" from three dimensions to two because the third relative coordinate for all of those things has to be the same.
Which is when relative motion becomes a problem. The Empire State Building and the Trump Building are at approximately the same altitude (i.e. sea level) but you don't have to worry about them crashing into each other because their relative position doesn't change. In space everything is in relative motion which effectively costs you another dimension.
Then you no longer have "space" you just have "a line" and if two things are at the same point on the line, they eventually crash into each other.
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.
The things in geostationary orbit don't crash into each other, they just constitute a relatively high density of "stuff" all in one place that non-geostationary objects at the same altitude could hit every time they cross the equator.
The worst case would presumably be something large and heavy put into orbit around the equator at the same altitude and speed as geostationary orbit but going in the opposite direction.
Which is when relative motion becomes a problem. The Empire State Building and the Trump Building are at approximately the same altitude (i.e. sea level) but you don't have to worry about them crashing into each other because their relative position doesn't change. In space everything is in relative motion which effectively costs you another dimension.
Then you no longer have "space" you just have "a line" and if two things are at the same point on the line, they eventually crash into each other.