You may be right, but if that happens the resultant space debris will serve as an additional terrible outcome of any major conflict.
We will have to kiss goodbye to any future space launches, existing satellites are likely to get knocked out and ultimately our frontier space era will grind to a hault.
You pretty much have to do this to knock out starlink (or similar constellations in future). There's so many currently deployed and they can be launched with such cadence that knocking them all out isn't feasible.