Andy:
Of course that would be stupid - but it's a rare person who hands over the keys completely!
In the end YOU hit the shots - the final decisions are thus YOURS, however you treat this. I have at times had a caddie so good, at a place so new or odd to me, I have ceded control and just tried my best to hit where he aimed me. But that is a rare event indeed. And even at those times, well.. the choices are discussed and reasoning understood, and in the end my choice is to trust him, he knows the course far better than I do.
In terms of strategic choices, hell it would take a VERY important match for me to give that much credence to such, but yes, those might get discussed as well. I can't see ceding that part of it wholly to the caddie... at most that has to be a consensus.
What I have done from time to time is cede control of reading of putts - but that too is a rare thing - and I do that only because I find I am not very good at it, or at least, I concentrate on stroke better when I have someone else taking over the reading part. I've had some darn good putting days with caddies. But I've had bad ones as well.
In the end, I'm with those who treat golf with caddies as something that can only add to the experience. It damn near always does. But to let it be a detractor... man unless the caddie was abusive or rude or something, I'd say that's the fault of the golfer.
TH