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.

Kessler syndrome isn't magic. Space is big. Starlink satalites are small. And they're low enough thst atmospheric drag will deorbit must of the small debris very quickly.

I disagree.

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.