You're making the single most common misunderstanding of the United State's ICBM defense capability, because you assume the goal is to "defend every city".

The real goal is quite different. The math starts to look very different when the defender can choose where to defend.

Assume a first strike against the US. The US has ~400 siloed missiles and a handful of airbases that can launch bombers. A reasonable goal for a first strike is to destroy those, preventing or substantially limiting a counterattack. Assuming some failure rate, using 2 warheads per silo gives you some redundancy, so 800 warheads needed for this phase of the attack.

What good is 40 intercepters against 800 incoming warheads? The US can choose which of those 800 to target. 40 intercepters can protect 20 silos from two incoming each. And that means the US can counterattack. To guarantee killing every single silo, the attacker must now have 20+2 warheads targeted at every single silo. The attacker has to build far far more offensive weapons than the defender needs to build intercepters, if the attacker wishes to avoid a counterattack.

Protection of the population comes from MAD alone, not by interception. (this of course isn't a reassuring thought, so this case isn't really made to the public).

That is why maneuvering hypersonics are considered such a threat: it removes the predictability of which warheads are going to land where, preventing that kind of choice of where to defend.

Strategically, the ICBM fields are warhead sponges. Each one only has a single warhead, but you'd want to target each of the silos, plus each of the launch control centers with more than one warhead, in order to keep them from launching. So a missile squadron would get hit with something on the order of 110 warheads in order to keep 50 warheads from launching.

But there are other strategic targets in or near cities. And those, it goes from having 2 warheads each, to havine 20+2 warheads each. So for the cities that don't get defended, it really sucks. But now instead of 1550 warheads hitting ~750 targets, it's 1550 warheads hitting ~75 targets. Because the attacker doesn't know what's going to survive to the target and has to choose their top targets that must get plastered.

Except it's worse: AEGIS BMD ships can launch from pierside. They don't have the range to defend the entire US but do for about half the US. So that's another wrench in attacker's plans (exactly how many SM-3 can hit depends on how many missiles are available at that time, which is a much more difficult thing to determine than the number of GMD interceptors).

MAD isn't a military doctrine. You won't see it on any doctrine publication of any service. The problem is the "Mutual" part. We don't want to die for our country. We want the other poor bastards to die for there. It's merely "Assured Destruction".

The US doesn’t need missile defence to maintain second strike capability.

That’s what SSBNs are for.

Indeed, which is why it is a bit silly to spend so much money on both. And yet the US does.

Silly if military prowess is your goal. Brilliant if funneling money to the military-industrial complex, garnering huge donations from lobbyists and making sure that all your friends and extended family are guaranteed lucrative careers is the goal.

THAAD is what you deploy to a place like South Korea where that 200km radius covers the entire country. For protecting something like the US mainland, you would use GMD, which can cover large sections of the continent.

But even if you did just have to build large numbers of short range interceptors, that's still perfectly acceptable. Likewise for upkeep and maintenance. You don't need to protect everything, you only need to protect the targets that justify the cost.