Or why try to shoot them down when you can also go to the command center and turn them off? Or do a targeted strike on said command center. The sattelites are plentiful and redundant, but the network will collapse very quickly when they're no longer controlled from the surface.

In fact, if SpaceX can no longer do any launches due to whatever reason, Starlink will no longer be feasible after a few year - if I'm reading it correctly, the sattelites have a lifetime of only 5 years, meaning they will have to continually renew them at a rate of 2000 new sattelites a year.