Musk's stated goal for Space X is to colonize Mars. His stated goal for Starlink is to fund said colonization. I 'm not so sure that he would enable any competition that he saw as having the potential to pose a real threat to his ultimate goal.
I've been ok with the tesla-only superchargers, because they are good. But it is a self-serving infrastructure and a competitive advantage.
I wonder what the reality would be about sending up bezos's satellites? It could also be a PR problem, PLUS it would undermine the bezos employees working on their launch platform.