Yeah, that occurred to me as well, though I don't know much about how the satellites communicate with eachother. I imagine each constellation would need its own band, but not sure how wide it needs to be? Intra-constellation communication could feasibly be done with lasers, in which case, all they may need to worry about is the Space-to-Ground leg. So maybe it's not too bad? I don't really know, but certainly interested in learning more...
That is, if we had an very large number of companies wanting to create satellite internet constellations, we would run out of useful EM spectrum before we would run out of LEO orbits.
I'm not positive about that, though!