I mean the assumption is that if the first missile hit the building, the second missile would have been fired at something else, right? Still seems worth it at face value especially if there's enough time between the two missiles that there aren't people in the building anymore.
This is why the superpowers mostly scrapped their ICBM defenses in the 70s. The technology worked fine. It's totally doable with 1970s technology if you're willing to put nuclear warheads on the interceptors. But for every ICBM interceptor you built, the other side could build another ICBM for the same cost or less. And you need more than one interceptor per ICBM since they can fail and the each interceptor only covers a small area. Add in multiple warheads on a single missile and decoys and suddenly you might need 10x or more. So the USA gave up on the idea of covering the entire country with interceptors, deployed a few interceptors to protect some missile silos, then shut it down after less than a year. The USSR built out a system to protect Moscow and only Moscow, which is still operational today. However, the British were able to maintain the ability to defeat that system and destroy Moscow with a single submarine, all on their own, never mind what the USA would throw at it.
If you have a certain amount of stuff you can build and you're deciding what to do with that capacity, it's not at all clear that missile interceptors are a good use of that capacity even if you're protecting objects that cost orders of magnitude more than the interceptors cost. It works if you're defending against a far less capable adversary (Israel's Iron Dome against Hamas, USA's GBI system against North Korea) but not with an enemy that's even vaguely close to being a peer.
Maybe it is possible. It does seem like it may be possible to defend against cheap drones with cheaper systems. Use lasers or good old-fashioned projectile guns instead of interceptor missiles.
For defending against proper missiles, I don't see how it's possible with any near-future tech. Guns and lasers don't work. You have to use a missile and it's going to have a cost similar to the cost of what you're shooting down. Peer enemies will be able to out-build you and many missiles will get through your defenses.
Shooting some down is better than shooting none down, but your enemy won't ignore your defensive systems. Shooting down 1,000 and having 1,000 get through is not better than shooting down 0 and having 1,000 get through. If building defenses just provokes the other side to build more offense, it's not worth it. If they're going to build the same amount of offense either way, then it might make sense to build up defenses.
Here's something to consider. The US has interceptors capable of shooting down ICBMs and with enough range to protect the whole continental US. There are currently 44 such interceptors. They cost about $75 million each. Standard procedure is to shoot four interceptors at an incoming missile to increase the likelihood of a kill, so that's about $300 million per incoming missile you want to counter. That's very much worth the cost if it prevents a nuclear warhead from reaching its target.
Russia and China together have maybe 700 ICBMs if we take a high estimate. For $210 billion, we could have enough interceptors to shoot down almost all of them. Round it up to $300 billion to account for all the infrastructure they'd need. That's a bargain compared to saving hundreds of American cities. So the question is: should we do it? So far, the American government has said "no." I agree with them, despite it being a bargain. Do you?
These cost ~$30M. They are in the process of scaling up production to a few hundred per year, with some help from the Japanese. Unit costs are coming down. These same missiles are also being deployed for land-based ballistic missile defense, despite their naval origin.
In the long-term you are seeing a convergence of the missile platforms as more capabilities are compressed into fewer missile designs. The US is pretty clearly evolving their systems to more of a “missile truck” architecture that is optimizing for the number of targets they can kill simultaneously at the maximum ranges that make engineering sense. Many aspects of new platforms like the B-21 all point in that direction.
A historical limitation is that the rocket motors used by most air defense missiles really weren’t adequate for ballistic missile intercept purposes. The US has invested a lot in closing that gap.
What are you referring to here?
More recently, they upgraded to newer missiles which could carry 8 warheads each, allowing them to overwhelm Moscow's defenses without decoys.