Why would you need to shoot down all or even most of the satellites? Pop a couple, let the resulting debris fields do the rest.
Considering that StarLink satellites have a orbital period of ~95 minutes, I doubt that debris fields de-orbiting "very quickly" as you so precisely put it will be quick enough.
And even so, just shotgun your payload of tungsten flechettes into a orbit a bit higher than the satellites and let gravity do the rest.
I'm sure people smarter than me have considered these scenarios and done the economic math.