That's not technically impossible, but comes with its own slew of problems.
To name a few...
1- Safety. GOP panels are in physical locations and need to be operated with a key. A RC can be stolen from a guard and used by miscreant brats. While stealing keys (or just buying them second hand on eBay) is not impossible, there's a smaller chance of wreaking havoc with this as it can only be done from physical locations and it's easy to spot when an unauthorised person uses a GOP.
2- The live railway is a tough environment. How much of a guarantee is there that the remote control will work properly under all conditions, even when in a confined space (underground station) or when you're standing on an overhead electrified line? AC is known to cause interference issues, is the RC system immune enough to that?
3- A remote control will have to work with one train at a time. If there's two trains of the same design in a platform, pressing [close doors] should not close the doors on both. Thus, a pairing mechanism has to be created to couple a RC to a train.
4- However, a train can be formed of multiple units. The remote will have to work with the entire train, no matter where the guard is standing. The pairing mechanism should be smart enough to work from wherever the guard may be standing, but should stop doing so when the train is divided.
5- Since RCs are moveable objects, it's inevitable that pairing has to be redone every now and then. That means some more staff training. It also means that there'll inevitably be disruption caused by a loss of pairing and unfamiliar train crew not succeeding in re-pairing RC to train. Is that acceptable?
6- A remote control means that it'll have to have a battery. What are you going to do when the battery dies midway through the shift?
7- RCs will inevitably end up getting misplaced or lost. What if guard 1 books off and by accident takes the RC home with them? Half an hour later Guard 2 books on and has no RC for the train they're supposed to work. Can the service still run?
8- 5 to 10 years from now, many RCs are likely to be in a poor shape and need to be replaced. Does the manufacturer of the chosen system still supply parts for it? Or even worse, does the company itself still exist?