Earlier quoted context omitted.
I took a screenshot of the default view on my web browser. The satellites appear to be around 100km in diameter, but they are in reality 7m wide, so they are 14,000x larger on the map than in reality. The entire constellation would fit within 0.2% of one of the white dots as they appear in the map. Then you need to remember that the space is 3D, unlike road surfaces (ignoring bridges etc.)
Space is not really 3d in the intuitive sense from a packing perspective, because satellites take up orbits rather than stationary points and orbits don't pack densely. It's more like an embedded 2d space, the intuition for that being that a ring, think Saturn's, is 2d and intersects any orbit.
Also, mean free path in a particle cloud depends on number density, cross sectional area and speed. The cross sectional area is small, but relative speed is also very high, which makes collisions more likely than one would think just based on their number density.