If someone starts taking out the 24 GPS satellites - a new anti-satellite weapon, or an interceptor satellite like the X-37 is speculated to be - being able to do it off Starlink's thousands as a backup would be extremely appealing to the US government.
(After all, this is the same organization that's happy to pay out the nose to keep ULA alive to have redundant launch options.)
It is not that simple, the high orbits mean it is very very difficult for solid propellant based ICBM variants to reach with a meaningful payload, also given the orbits it is much easier to perform early detection and make evasive maneuvers.
Also remember even if you did launch on liquid rockets, It is not easy to launch them in quick succession or with stealth. Liquid rockets needs a lot of time to load fuel, needs a ton of auxiliary equipment( cryogenic fuel storage at-least) and have limited shelf life once loaded which means they are limited to few known sites which you can quickly take offline after the first attack/launch.
Solid rockets/ICBMs can be launched from variety of platforms some of them very mobile and also given their lower footprint - Silos and other sites can be hidden and missiles moved around to retain the strike capability.
ASATs are primarily designed to target low flying spy sats[1], taking few key ones out can at the right time can potentially deliver few hours of advantage in a battle before alternative sats can be rerouted. Communication and navigation sats on the other hand are designed to operate even during normal times when few go offline without loss of operational capabilities .
[1] Also this is much easier to justify domestically and globally than say communication ones even if they were dual use.
