The defense shield is mostly a symbolic issue. Missile interceptors and radar stations in Eastern Europe can’t possibly be used as a protection against Russian nukes.
I’ve read a Russian general’s opinion on this, which explains why hey are so pissed with just 10 interceptors. I don’t know how much of it is factual, but at least it explains their position.
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As you noted, there is no way to stop thousands of nukes with this shield. The only scenario when the shield against Russia does make sense is when most of Russian ICBMs are already destroyed.
Since the invention of spy satellites the location of strategic missile silos of the all countries is largely not a secret. If US uses nuclear submarines to attack Russian ballistic missile silos, Russian retaliation options will be limited to a few mobile ICBMs. And then the proposed shield in Eastern Europe becomes highly effective: it can intercept up to 10 ICBMs on early stages, before they split into warheads (could be 200 warheads in 10 missiles).
Any US domestic anti-missile defense has to deal with individual warheads. Even 10 ICBMs if allowed to leave Europe are a very serious danger, since realistically it’s not possible to stop even half of the 200 warheads heading towards US cities and military installations.
Also, once the shield is in place, nothing will stop NATO from turning 10 interceptor missiles into 50 in a very short time.
So basically the only scenario when this shield is useful against Russia is during an offensive strike, greatly increasing chances for such a strike to go unpunished.