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.
I would expect the bandwidth demands of the US military to be effectively infinite. Especially if the connection can be guaranteed and is low latency.
Communication is incredibly valuable in maneuver based combined arms warfare. The main limit is being able to quickly react and properly coordinate. For that comms are important, and reliability of comms is incredibly valuable, with latency being important as well.
Starlink has the very nice feature of being robust, just by virtue of having soo many satelites. China can easily knock out 4 geostationary satellites. But hundreds of low-orbit satellites make for a very difficult target.
The DoD has far more than just 4 satellites. Anyway Starlink satellites are really low making them much easier targets.
I wouldn’t be surprised if a single HARP style light gas gun couldn’t cheaply take down every Starlink satellite for a few hundred million total. The best defense is having a wide range of satellite orbits and the ability to quickly deploy more. If nothing else, a single nuclear EMP could wreck a huge swath of the Starlink network.
The DoD has far more than just 4 satellites up there.
Anyway, it’s vastly easier to destroy LEO satellites than Geostationary ones. A surprisingly tiny missile fired from an aircraft doing Mach 2 can take out Starlink satellites as you only need vertical speed the satellite provides energy at collision, but geostationary orbit takes significantly more. https://en.wikipedia.org/wiki/Anti-satellite_weapon
From the sources I looked at, NDSA is supposed to be less than 1,000 satellites by 2030 which isn’t a huge jump over what they already have. They just don’t benefit from that kind of satellite density at the bottom of LEO when it comes at the cost of lower lifespan.
What they want from NDSA is multiple different systems each with a separate focus that can all use a uniform transmission layer.
Starlink has more total bandwidth and lower orbits, but the US military only needs so much bandwidth.