yeah, certainly it's possible to have turnstiles that know where you got on, DC and London and Paris do it.
But first, think of the capital investment, it would be huge. The MTA has no way to source that money. Second, most of the platforms outside the city have a zillion access points. Fordham and 125th would work because there are so few ways in or out but nearly all the ones in the suburbs would be impossible to "secure." Even if they could afford to build all those electronic turnstiles, it would still be ridiculously easy to bypass them unless they somehow walled off entire platforms for hundreds of yards, multiplied by dozens of stations.
Finally, imagine the lines it would create. Hundreds of thousands of people stream through GC every day and never stop until they get on their trains. If you bottlenecked the tracks at each end, that would be a massive headache.
Amtrak does not allow you to buy tickets on the train and there are no turnstiles but they do check your ticket before they let you on a train and it creates a pretty big backup. They have many fewer trains that GC/MN.
I just don't see how this would work.