If I thought it was unsafe I wouldn't board.
However I would imagine standing tightly compact is safer than standing with loads of space. In say an emergency stop, if there is loads of space around you, you'd get thrown about, but if tightly compact there is nowhere to be thrown about.
....and if there's a fire or need for swift evacuation involving a train that is so overcrowded and packed that people can't move to the exits quickly enough?
Good point. It's often forgotten by those who say overcrowding is safer in an incident with a train, that not all potential incidents are ones involving rapid deceleration. Fire and/or smoke in a confined space are very dangerous when people are trying to escape quickly.
And a relatively light impact could cause quite a serious crush of people flung in the direction of travel on a packed train, whereas if everyone was seated it probably wouldn't be an issue.
I shudder to think of the mess if there was a high speed collision/derailment on one of these heavily overcrowded services.
Re: the London Underground, the trains are designed with standing in mind and thus have many more grab handles and such like for standees to steady & secure themselves and much larger open areas throughout the vehicles to allow circulation space for people leaving/joining the train & standing. Train speeds are, in general, very much lower than mainline trains, so it is a very different environment overall.