With the double doors the persons trying to catch the train no matter what will slow the closing of the doors much more I suppose. Some people might remain with bags, umbrellas etc. "in between".
Now that I think about it, one of the things that slow underground train operations is that people must first get off, then people can get on. People trying to get on, in crowded stations and situations, are an obstacle to people getting off.
With modern trains which have carriages communicating with each other (a long "snake" where you can walk freely) tube trains could be optimized so that let's say the first carriages are for getting on only, and last carriages are for getting off only. That would make the pavement traffic "one way". All the internal paths of the tube stations could be optimized so as to avoid double senses of circulation.