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.