I'm sure if you'd like, they can....by doubling the price. It isn't cheap for hertz to move cars at all. Even the most simple runs (within an airport--between lots) take 10 minutes roundtrip. In addition to someone to pickup the car, you need a van and driver to take them to the source--and to drive back. Lastly, and this is NYC-specific, is the (potential) cost of tolls associated with driving a car across the city, depending on the route you use.
Oh, and you obviously can't rent a car while you are driving it across the city because it is already in use.
I looked at the times driving from EWR to JFK/LGA and it looks like a 2 hour round trip, accounting for decent traffic speeds and having a caravan of cars traveling together. So, every car moved probably costs them $30 in hard costs (gas and wages) plus lost rentals. JFK-LGA is a little different---but even at half that cost, it isn't cheap.