suppose one has N independently developed interception systems (from detection till physical interception attempt), each with an intercept success rate of 90%.
a rudimentary calculation then gives the probability of hitting (not sinking) the ship as 0.1^N per launched missile; so it seems that given enough budget to spend on independently developed missile interception systems allows to drive down the penetration success rate arbitrarily.
Multi-billion sounds like $ 10^10; so assuming an attacker can launch say a million missile attempts then the statistical loss would be 0.1^N * 10^10 * 10^6; so the statistical loss can be driven down arbitrarily say to $ 1 by developing ~ 16 independent interception systems.
16 independently developed intercept systems doesn't sound like unobtainium for a vested nuclear power.
furthermore, the development cost of 16 independent intercept systems can be amortized over many more installations than a single ship, it can be amortized over multiple ships, multiple bases, multiple strategic assets across the globe.
You have abstracted things a bit too far.
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.
equally unobtainium as the 1 M missiles aimed at the ship.
Is it? Russia’s making 60k Shaheds a year, and they are in the middle of an active conflict that has other needs.
60k / year = about 180 per day = 7 per hour.
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.
You’re proposing largely experimental or theoretical solutions to a today problem.
And the Ukraine war has demonstrated the issues with jammers.
I agree launching 1 M Shahed drones at a ship would be purely theoretical, and won't solve Iran's today problems...