A ABM interceptor will cost much less than a ICBM with a nuclear warhead.
The missile about the only place where an ABM is cheaper.
The missile is much smaller and doesn't even have to have a nuclear warhead and even if it does have a nuclear warhead it will be smaller.
Without a nuclear warhead, you need very precise guidance to ensure the conventional warhead gets close enough, or the kinetic warhead achieves a direct hit. Modern ICBM warheads come in much faster than SRBMs, cruise missiles, or even long range missiles from the 1950s and 1960s. Sure electronics have improved, but you are still trying to hit a very small and very fast missile with another very small and very fast missile.
Even if a ABM system cost 1 Trillion dollars the system is protecting tens of trillion dollars of US economy. So you argument that a ABM system makes no economic sense is false logic. ABM system make perfect sense under any situation.
Except the issue is that each interception is another attempt at protecting that asset, and the system is likely to degrade over time. It also gets back to how defensive systems work on probabilities, not certitude. A low probability of total destruction is pretty good for the attacker, not so good for the defender.
Suppose you have a system that is 80% effective. If it's defending a target of moderate importance, twenty or so warheads will come in. That's four probable failures. It doesn't matter how much value was saved by the first sixteen successes if it's all lost on the last four. Then you consider that all they have to do to increase the probability of destruction is throw more warheads at the target (possibly as simple as one more than ABMs available), and you can see why in a MAD scenario ABMs don't work.
If you aren't in a MAD scenario, you can build ABMs because you already have nuclear supremacy, and can afford to take away from your offensive forces (this is why the United States and Canada looked into ABMs in the 1950s and 1960s). Once MAD becomes reality, and you don't have an ABM, deploying an ABM system that actually works threatens to break the MAD system, lead one side to have an advantage, and create a window for a (more) successful first strike. Knowing this, why would the other side wait for the ABM system to be deployed? They would strike first.
Game theory isn't nice, but there are logical and economic reasons why things went they did on the nuclear strategy front during the Cold War.