They already have global coverage via a range of communication satellites used by various programs going back decades. For example the F-16 program had an independent network for effectively global coverage via 4 geostationary satellites. Other systems used polar orbits for actual global coverage.
Starlink has more total bandwidth and lower orbits, but the US military only needs so much bandwidth.
Starlink has more total bandwidth and lower orbits, but the US military only needs so much bandwidth.