You have it backwards. All helicopters should not be with IAF, in fact all should be with AAC. Only few SAR/SOF helos should be with IAF.
Currently we are working with the mindset that anything that flies belongs to Air Force which is an outdated model. Modern force allocation should happen on basis of combat role & requirement, which is what happens in countries which follow NSS type white papers.
RAF & RN are pooling resources to create Lightning Force HQ (on the back of old Joint Force Harrier), providing not only common infrastructure, but common command & control and training resources for F-35s across air force & fleet air arm. That's how jointly you get to operate, and that's how much money can be saved by jointmanship.
en.wikipedia.org
The current policies of our's are disjointed, each force is fighting it's own war. Theatre Commands, NSS, etc. these are all policy decisions designed to fix that very problem.
Well then the US must be insane for creating such things as unified combatant commands, NORAD, joint transportation & logistics nodes and creating SOCOM.
Think.