ICBMs are multiple orders of magnitude faster. It is basically impossible to intercept an ICBM in the terminal phase, except with nuclear interceptors, and eve

ICBMs are multiple orders of magnitude faster. It is basically impossible to intercept an ICBM in the terminal phase, except with nuclear interceptors, and even then. So you need high altitude interception. The problem is that it's really easy for ICBMs to decoy themselves when they are out of the atmosphere. For example, simply wrapping the warheads in a much larger Mylar balloon and then packing a few hundred identical balloons that are empty makes interception basically impossible - you're going have perhaps a few hundred thousand targets to intercept in case of a nuclear strike, which is simply impossible. By the time the balloons pop or slow down enough in the atmosphere, it's essentially too late. The other alternative is early interception, but the only relatively credible design for that is hundreds of nuclear powered laser satellites. Which poses the issue of those satellites themselves being overheated by lasers and disabled in seconds.