To answer your question about people travelling in and out of London by train, DH and I live up north and travel by train to visit family in London or the SE (which will involve changing stations in London). As train tickets are expensive, we usually book advance tickets which mean we have to get a particular train or pay extra. So it's quite likely that if we'd rushed past you in a London train station, it's because we're in a rush to get a train and don't have the time to walk behind someone who is walking (understandably) slowly.
These visits are usually for a few days, so we'll have luggage, and space for luggage is annoyingly limited even on long-distance trains (Virgin trains, I'm looking at you!). So it is irritating when people shift your luggage to make space for their stuff.
Your assumptions about people who don't need to use the lift are rude. I have joint problems, so sometimes stairs are an effort. Or when I was in early pregnancy and exhausted, I couldn't manage the stairs. I might have heavy luggage and need the lift, or I might just want to use the lift!
Likewise, on a long train journey I don't necessarily want to be chatty and sociable to anyone. Often I want peace and quiet to read and relax, so I usually book tickets in the quiet coach (DC1 is due soon so relaxing train journeys will soon be a thing of the past!).
DH will often offer to help people getting on/ off trains with luggage/ prams, but again, only if we have time and aren't rushing to make a connection.
Of course, I may be making the same complaints as you in a year's time...