It doesn't matter if it's the only option if it's not possible to do it.
Maybe it is possible. It does seem like it may be possible to defend against cheap drones with cheaper systems. Use lasers or good old-fashioned projectile guns instead of interceptor missiles.
For defending against proper missiles, I don't see how it's possible with any near-future tech. Guns and lasers don't work. You have to use a missile and it's going to have a cost similar to the cost of what you're shooting down. Peer enemies will be able to out-build you and many missiles will get through your defenses.
Shooting some down is better than shooting none down, but your enemy won't ignore your defensive systems. Shooting down 1,000 and having 1,000 get through is not better than shooting down 0 and having 1,000 get through. If building defenses just provokes the other side to build more offense, it's not worth it. If they're going to build the same amount of offense either way, then it might make sense to build up defenses.
Here's something to consider. The US has interceptors capable of shooting down ICBMs and with enough range to protect the whole continental US. There are currently 44 such interceptors. They cost about $75 million each. Standard procedure is to shoot four interceptors at an incoming missile to increase the likelihood of a kill, so that's about $300 million per incoming missile you want to counter. That's very much worth the cost if it prevents a nuclear warhead from reaching its target.
Russia and China together have maybe 700 ICBMs if we take a high estimate. For $210 billion, we could have enough interceptors to shoot down almost all of them. Round it up to $300 billion to account for all the infrastructure they'd need. That's a bargain compared to saving hundreds of American cities. So the question is: should we do it? So far, the American government has said "no." I agree with them, despite it being a bargain. Do you?
The US Navy is largely responsible for long-range ballistic missile defense, since you have to cross an ocean to hit the US. They also have among the most sophisticated missiles for that purpose, capable of killing an ICBM at apogee. The inventory of these missiles is much larger, every destroyer carries them, and recent variants are often considered the most competent of the various ABM platforms out there.
These cost ~$30M. They are in the process of scaling up production to a few hundred per year, with some help from the Japanese. Unit costs are coming down. These same missiles are also being deployed for land-based ballistic missile defense, despite their naval origin.
In the long-term you are seeing a convergence of the missile platforms as more capabilities are compressed into fewer missile designs. The US is pretty clearly evolving their systems to more of a “missile truck” architecture that is optimizing for the number of targets they can kill simultaneously at the maximum ranges that make engineering sense. Many aspects of new platforms like the B-21 all point in that direction.
A historical limitation is that the rocket motors used by most air defense missiles really weren’t adequate for ballistic missile intercept purposes. The US has invested a lot in closing that gap.