Why is Tanks kill Tanks a sound doctrine?
Simple. Tanks hunt each other first. Once the enemy armor is out of the way, the friendly tanks do the infantry support thing. The thing that disguises this practical application of tanks is that in order for tanks to go hunting, they need friendly infantry and air bodyguards to protect them from the most efficient tank killers out there... well trained enemy infantry. Hence the combined arms mantra that all armies preach but few armies practice.
That sounds like planes kill planes.
Exactly. But I would say your friendly air force kills the enemy air force first, and then it does the infantry and tank support thing. (Combined arms again.)
Wouldn't you rather your tanks were out there conquering territory, advancing and leap frogging enemy positions and doing a combination of blitzkrieg and infantry fire support?
Tanks properly can't conquer territory without a lot of protection (infantry and air cover).
Why not leave killing tanks to the experts, as in, A-10's and Apaches and get on with the conquest?
Because AAA and enemy air power interfere with the kind of slow and close attack runs that helicopters and A-10s have to practice for cannon and missile kills.
. PGM munitions in the Iraq wars near missed T-72s by as little as 3 meters. The blast was enough to kill the tank crew, but the tank was still usable. Bombing is no guarantee that a tank will be wrecked. You have no doubt when you see a T-72's turret fly off after a sabot round lights off the ammunition carousel at the bottom of the fighting compartment. Thermal image through a M-1's gunsight can be filmed for a BDA.
Because aircraft and helicopters are transitory platforms that do not have a permanent controlling presence that a piece of mobile armored artillery designed to kill its opposite has.
Because a tank can fight in a sandstorm or blizzard or a typhoon. Just as long as it can roll and shoot it is persistent and immediate. You have to call in for artillery a helicopter or airstrike. You can get dead in a hurry waiting for the fire or bomb mission to arrive or the weather to clear. Mister Tank is right next to you and all you have to do is pick up the phone on the fender...
As for Iron Dome, it's be useful for US army if it and its various components (C&C, radar) were mounted on trucks and could be easily deployed from base to base. I think (but not sure) that all Iron Dome components are mounted in containers? If thats the case then its a useful weapons system. If thats not the case, then no one outside of Israel can really use it.
Iron Dome has canister missiles, truck mounted radar and a battle management center that is carried in vans or shipping containers. It is entirely mobile. It is eminently suitable for containerized movement. I would go so far as to say it could be a good fit for an expeditionary force as such a modular system could be added as a bolt on to STUFT shipping and used both afloat and ashore.
Previously the Americans were looking at something like a Phalanx or a particle beam weapon as a base defense, but Iron Dome manages to cover a larger radial defense zone foot print more cheaply and with a beter intercept change in mid-phase than either descent phase American system.