Shot exchange is a huge problem, made even worse by the arrival of cheap drones. But you're implicitly assuming that the adversary is on roughly equal economic footing. If your defense budget is $800 billion and your adversary's defense budget is $8 billion, you can afford to spend 100x as much shooting down their missiles as they spend lofting them.

There's also a danger in projecting linearly from the beginning of a war, where invading forces both tend to use more expensive stand-off munitions and also have to deal with more aggressive missile launches. As the defender's own air defense system gets degraded, the invader can switch from expensive long range stand-off munitions to cheaper stand-in munitions (like glide bombs) launched from much shorter range. Additionally, the invader will be able to diminish the defender's ability to launch missile strikes in the first place, either by destroying the launchers, the missiles themselves, or their production, thus reducing the demand on expensive high-capability interceptors.

Drones and mines continue to offer asymmetric warfare options that are very hard to counter without a robust low side on the high-low mix. Ukraine are the world's leading experts in this currently, and hopefully are involved with US and Gulf forces to try to improve this shot exchange ratio.

I am assuming nobody is using nukes though. That completely changes the picture. One must always assume "(some of) the missiles will get through". Traditional MAD does not require boots on the ground - merely the assurance that if Iran gets one nuke through and hits New York, the USA will respond with 100+ nukes. The real question then is what the other "large" nuclear powers (Russia and China, primarily) will do in response to that.