Remember that this space is significantly larger than the total surface area of the Earth, since it represents a sphere larger than the Earth. Imagine the satellites are the size of an outdoor garbage receptacle. Do you think 600+ of them floating around really presents some risk of collision? There's probably more garbage bins just in New York City, and this is spread over an area much larger than the surface of the Earth.

Space is really, really large. Using the intuition you developed while living on the surface of the Earth provides you little help when thinking about space.

The asteroid belt, which is positively TEEMING with possible collisions... billions of objects... yeah, we don't even bother. Ninety-nine (point nine nine nine...) times out of a hundred you won't hit anything. Space is big.

Well, to be honest, orbits are more like corridors so the risk of collision increases a bit. But still, if they're at least a little bit careful about avoiding generation of space junk, there shouldn't be a problem.