There will always be a very small number of idiots who behave in this way.
IMHO, there are a number of reasons why it's presently more than a "very small number".
There is a simmering mutual contempt between passengers and staff. Whether it be the high price of travel, not getting a seat, trains running late - many passengers are simply not happy to be on the railway and don't respect the industry.
You see posters saying how the doors close 30 seconds before the scheduled departure time - but then so often they don't. So often trains depart a few seconds after the scheduled time, or even a minute or two (and are still regarded as on time). So passengers don't respect the need to get trains away on time. Another few seconds won't make a difference, as far as they are concerned.
I'm most familiar with East Croydon. Passengers still have unclear information as to which platform to go to for, say, a fast train to Victoria. They go down the long ramp to platform 1, only to find that the next fast train is platform 4. Or a 4 carriage train comes in, and stops well beyond the end of the platform - so people have to run to make the end of the train. The passenger displays often don't show how long the train will be. Sometimes trains are removed from the displays as they become "ready to depart". Sometimes they are still showing well after a train has left. Even when a train is shown as expected on time, it can come in a minute or two late. So if you're on the concourse at, say, 15:00 and a train is due and expected at 15:00, you know it's probably still worth running for it.
On Thursday, I was travelling from East Croydon at around 5pm. A 4-carriage train comes in a couple of minutes late. Passengers stand back to let people off first, it's very full. Whilst people are still disembarking, the dispatcher starts blowing his whistle. What are people expected to do? It just ups the ante. Some people start pushing on whilst others are still getting off.
So we can talk new byelaws and even have yet more penalty fares and/or prosecutions. But I don't think it will help....