The economic problem isn't nearly as insurmountable as postulated: A GBI interceptor is ~$70M. A Sentinel ICBM is ~$140M. An NGI interceptor is ~$100M. So already, we see that the interceptors are cheaper than an ICBM (though admittedly about the same order of magnitude). Standard Missile-3 is $10M-$28M (depending on version)
But the cost of the missiles themselves are not the only problem: you have to pay for all the apparatus around the missiles. That's the silos, the command and control, etc. ICBMs demand silos that can survive near missiles from nuclear warheads. The launch control centers need the same survivability. Truth be told, we can't build more. We're refurbishing all of the Minuteman missile silos for Sentinel. You need these to survive to the end of the world, so that you can make sure they people who ended yours also have theirs ended. You also need not just survivability, but assured control. An ICBM launching is the start of a nuclear war. We need to make sure that it doesn't start by accident. The net result is that the Sentinel program is $141B for 659 missiles in 400 silos).
Contra wise, an interceptor needs protection from the elements and maybe special forces attack. By the time the end of the world has come, they have all launched. So the silos are comparatively cheap. The launch control center is cheap. If a missile is launched by accident, it's just money (and a reduced amount of potential defense). It's not the end of the world.
GBI and NGI are National Missile Defense systems. The defended area is limited, but to say that is to underrate how much area is defended. It's all of North America. SM-3 Blk-IIA has a defended footprint equal to half the US (as in, a ship just outside SF Bay can defend out to Nebraska; a ship at Hampton Roads can also defend out to the other side of Nebraska) [0]. NGI even is designed for multiple kill vehicles. Which is to say, it kills multiple MIRVs.
But the problem is that the cost curve is actually the reverse of what you assume: if the warhead can't always get through, and you have to choose where your warheads land, and you don't know which ones won't get through, you have to assume that the defender might just decided that the target you really want dead, is the target they really want to protect. So if the US has 40 interceptors, and can shoot down an estimated 22 warheads with them, I have to paste the Pentagon with 23 warheads to make sure that it's dead. So the other 22 targets that were going to get hit, no longer can get warheads allocated to them. This applies to every other target the Russians want to kill. So suddenly, they don't have 1700 targets to hit with 1700 warheads, they have 74 targets. It will really suck to live in those 74 targets, but the other 1600 some places on the target list are going to be better off. And to hit another target, the Russians would need to add another 24 warheads to their ICBM force. But to force the Russians back to distributing those warheads among the 74 targets, the US would have to kill an average of another 1/3 of a warhead. Recall back that the SM-3 Blk IIA is ~$28M, while a Sentinel ICBM is ~$240M per deployed missile.
This doesn't even get into how the interceptors force the ICBM MIRVs to become less accurate, or hypersonic boost glide vehicles being limited to 1 per launcher, or the fact that we can track HGVs for the entire route, and decoys don't work for them.
0: https://breakingdefense.com/2015/07/aegis-ashore-navy-needs-... image near the bottom shows footprint of IIA