Unless your interceptor system is unobtainium laser system with unobtainium cooling system, backed-up by unobtainium power source, you are going to run out of interceptor missiles (or even Phalanx bullets) way sooner than 'million missile attempts'.
Quite possibly 100-200 Shaheds + half a dozen proper anti-ship missiles will cause you to turn tail.
there are so many options from coil guns, to lasers, to jammers, to non-nuclear EMP's, ... that don't involve the caricature of a million dollar missile intercepting it.
And the Ukraine war has demonstrated the issues with jammers.