With how close to earth Starlink satellites fly, it won't take hundreds of years. Without the occasional boost back into orbit, it'll only take a couple of years for them to fall back to earth. Same with most spy satellites. We can do without space internet for a few decades if we blow up several of these constellations.

As for further-away satellites (Iridium etc.), that's a bigger risk, but there aren't that many that make sense to target in a war.