There was a concept called "Brilliant Pebbles" in the cold war and it is the basis for the so called "Golden dome" project now. Basically you launch thousands of space based interceptors and spread them in LEO similar to Starlink, each interceptor has a certain delta-V available to maneuver.
Upon the detection of a launch, the interceptor that happens to be in the right place and the right time can maneuver to intercept it in boost phase.
There're reports that point out such a system is something of a lemon though and I tend to agree with them:
The gist is that time window for boost phase interception is extremely short (3 to 5 mins), very small portion of your space based interceptors is in range to respond. A geologically concentrated launch from even a small nuclear state (say DPRK) can overwhelm you defense. Keep in mind your typical interceptor is not feather light tiny thing like your Starlink sate, those are KKV with at least 4km/s delta-V, the cost to launch and deploy them in numbers is far higher than Starlink. A credible defense system of this type is not economically viable.
While "Golden dome" maybe a lemon in missile defense, it could be extremely potent in the role of space warfare and space blockade. This is where I think it pose the greatest threat should US is able to field it.