Out of interest which trains have you been asked to leave? I have seldom seen this done and, in all honesty, I would ignore any such instruction if I thought it possible to board.
I have never been asked to leave a train, or indeed never failed to board. I only asked out of curiosity, Just before Christmas I was on a packed XC service, when we arrived at Sheffield some 15 mins late, people started trying to board so the TM "suggested" some people may like to get off and catch the next service in around 20 mins time and have a less crowded journey. People were left on the platform at every stop as far as New Street, including a wheelchair user at, I think Tamworth.
Another occasion I witnessed was at Wolverhampton one evening a few years ago, again just before Christmas, when the TM on the XC service from Manchester announced that the train was not moving unless some people got off, he informed them there was a LM service in something like 10 mins time, I don't know if anyone got off but, the train was on it's way shortly after.