Ha! When I worked in London I soon learned to ignore tannoy announcements, which were often made for purposes other than to help passengers. For instance, waiting at Euston for a Northern Line train on a packed platform (because there'd been no train for quite a while) the standard announcement was "do not try to crown into this train. Another one is just a couple of minutes behind it and will not be so full".
Of course the next train was many minutes behind and crammed as well, but the announcement was made to limit boarding delay to the train in the station as everyone tried to force their way on board.
But how daft do the announcers think passengers are? You only fall for this once, then when you realise you've been 'had', in future you cram onto the first train that arrives - the next could be a long time behind and just as full, despite what the tannoy says!
While nobody can know the train behind is full or empty, you do get to make a pretty good guess over time - and if there was a long gap in service, it's obvious the next train or three will be packed. Eventually, you'll catch up with demand and the trains will have space.
So, far from thinking staff are playing with you, it is in fact good advice. Not that I need to hear staff telling me to wait. When there's been a long wait, and the next 2-3 trains are 1 minute apart - I am quite happy to wait the 2 or 3 minutes to get some air, and even the chance of a seat.
It is also sensible to wait as the quicker the packed train, that you can barely get on and will then be incredibly uncomfortable, can leave - the quicker the next ones can come in. It's the packed train stuck on the platform that causes delays, so why you'd think of ignoring good advice and trying to squeeze on is beyond me! Just wait for the one after if the next train is still busy - they won't all be busy forever you know!