I agree that it sounds unlikely that you would be charged extra for failing to collect the hire car. And considering that you don't see any such requirement in the contract, I think you're in the clear.

I've taken advantage of such discounts for many years and have never picked up the car or used the hotel. I have never heard of any such requirement and I've never had any negative consequences.

Perhaps the TA is wary as this scenario vaguely resembles hidden city ticketing, and the TA is concerned about being liable if the entire booking is not used…