We could still install PEDs with imprecise doors. Ie more doors than required. Larger doors than required. The main thing is for the door to only open while a train is in front of it, and all the train doors be unobstructed.
Ie won’t hurt much to have a PED open to the train wall or opens double the size of the current trains’ door.
I imagine there would be safety issues with that approach since it might create an opportunity for people to get trapped between the platform doors and the train. No sense solving one safety issue just to introduce another one. You'd also need to be sure the platform doors didn't take any longer than the train doors to open. Anything that increases boarding & alighting time, even by a second or two, would likely be rejected in London.