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.