Except it costs many times more to make an anti-ballistic-missile interceptor then the original ballistic missile.
There's a fundamental asymmetry here, because interceptors have to be extremely high performance to be useful but the launching missiles can be as cheap as possible as long as it can throw enough penetration aids into the approximate trajectory.
So regardless of how much is spent on such a program, any country could spend a small fraction to fully defeat it, maybe as little as 10%.
That doesn't sound correct to me. They're both rockets, one is much larger than the other and has a payload (in the case where we're looking at a failure of deterrence) made out outrageously expensive material. I mean, you can construct an argument that one is already built and paid for, or that 70's/80's technology was cheaper inherently, etc...
But from first principles, no. An ICBM is more expensive than an ABM.
Some subjects, like computer science, which is still a very young area of study are very open to learnings from first principles. Others, like the geopolitics of nuclear deterrence, are deeper than any one person can even begin to understand.
The objective of National Missile Defense isn't to stop all the warheads, it's to make the attacker's job harder. There's a bunch of ways it does that. One is that the defender gets to choose what it stops. So they can stop all the warheads going to one target. But the attacker doesn't know ahead of time, so they need to launch enough warheads at each target to destroy it regardless of whether it's actually defended or not. So 1550 warheads no longer hit 750 targets, but rather they hit 75 targets. It really sucks to be one of those 75 targets, because most of them get absolutely destroyed, but the other 90% of potential targets are much better off, because they didn't get hit at all.
Another way is that ballistic missile accuracy depends on how far away from the target it gets separated from the missile bus that has the guidance system. If they separate too late, the interceptor will hit the bus before separation. Which kills all the warheads. So they have to move it back, which makes it less accurate, which means it's more likely the warhead will miss the target.
A third way is that they may decide they need to carry penetration aids. But there's a bunch of really fancy tricks radars and IR sensors can do to see which is a real thing, and which isn't, which amount to: the penetration aid which is best at mimicking a warhead ends up being the same size and shape as a real warhead. So they might as well just use a real warhead.
The launching missile can carry dozens of penetration aids, each one needing an interceptor warhead.
Plus, the physical structure and fuel are by far the cheapest parts, it's everything else, guidance systems, maneuvering systems, etc., that make up the majority of the cost. Which each interceptor warhead needs but which dumb penetration aids don't.
I'd say that it's exactly the fuel, the engine, and the whole chassis of an anti-ballistic missile what's so expensive. An ABM has very little time to do its job. It has to launch instantly, and accelerates at 100g or so, and then must also maneuver at this circumstances. It should also pack enough punch to destroy a warhead which is a relatively small metal needle, built to withstand the mechanical and thermal loads of an orbital reentry.
As a contrast, an ICBM can start with much more soft acceleration, can spend 10-20 seconds preparing for launch without loss of efficiency, and does not have to maneuver much during ascent and the orbital part.
And remember that acceleration is what costs, not speed. To shoot down an ICBM you need to hit it with a similar mass at a similar speed, and you need to do it in less time (because the ICBM launched first), so your interceptor needs to accelerate harder.
To intercept a missile you need to intercept it - that's it. You don't need to be traveling the same speed, or have the same mass, you just need to be physically where it is at the time it's there.
ICBMs aren't armored - and they can't be. They're spacecraft of a sort, and doing almost any amount of intentional damage will prevent them from functioning. Nuclear warheads are hard to detonate - the behavior if disrupted is the weapon likely goes inert because you've ruined the implosion mirror or timing circuitry.
The problem is that interception is hard because your engagement times are very short, and you're off-trajectory. Initial deviations in your aiming create larger and larger errors at the target, and any sort of maneuverability on the warhead's part means you're unlikely to be able to correct in time - hence the focus on trying to hit missiles in the boost phase, when they're by necessity more predictable.
Why would it need to be a similar mass?
