European and Asian allies would have to start by investing in low-cost launch capabilities. So far they're making approximately zero progress in that area.

The reality is that all US allies except for maybe France no longer have the capability to project power much outside their own territory without active US support. It's not only satellites. They're also missing just about everything else such as logistics, specialized aircraft, air defense, amphibious capabilities, intelligence, etc. With largely stagnant economies there's no way they can sustain the funding necessary to close those gaps unless they join together in closer alliances with each other.

Most countries would not need to make their C2 infrastructure fully dependent on Starlink, because most countries are not big enough and cannot project enough power globally to make this an actual requirement, and the few countries who can project power globally can afford multiple communications layers. But your core idea is true.

This is explicitly one reason the US marketed the F-35 so hard to their allies. In addition to giving their allies a good capability, it made their air force dependent on continuing US support, so politicians wishing to go against US positions have to be willing to sacrifice their military power to do so. This gives the US a strong lever in negotiating.

LEO is pretty expensive. Smaller countries might be better off with cheaper Astranis GEO satellites.

That's valid and definitely changes the risk profile if the military constellation is operationally separate. Though the civilian network is still a force multiplier in many cases, which puts it in the targeting calculus for adversaries regardless of whether troops depend on it directly.