Yet I know cases when police returns a stolen car to it's owner, and never bothers to look for a thief, even though the car is left with a lot of junk (papers, receipts, personal items) that could lead to the thief easily.

And the cars are usually just found randomly, not really looked for.

Police choppers here fly ~ 2000 hours annually, I don't think that having them for 400 hours per year is going to be worth the price of buying them in the first place.

Helicopter usually in the air already it just respnds To the call like a cop radio

No. Police chopper bore holes in the sky because they're not needed 100% of the time but if they weren't already in the sky the response would be too slow. To the extent that they can remain in the general area they're supposed to sending them to look at less important things on the ground is actually a positive because it's less boredom for the pilots. Something hot comes up and they'll dash away from that stolen car.