I have seen horses try to leave through the escape doors- it isn't pretty.
However, depending on the horse, it might be more dangerous for the handler to attempt to squeeze past the loaded horse when it's on the straight load trailer. The escape door is for handler safety - giving them a place to exit that doesn't involve going around the back of the horse in a tiny straight load stall.
However, the escape door should be closed immediately upon exiting, and the horse should be properly tied, with a chest bar in front of him, so as to help limit this type of problem.
Personally, I view having a horse try to escape through the escape door nothing other than handler negligence, and not a problem with having the door itself.
I've seen it many times where people will be at shows, vets, or whatever, with their horse in the trailer and the escape door right next to them open so the horse can "get some air"...... then, before you know it, they get the chest bar down and have their feet out the trailer while their head is still tied. *That* creates the danger - ignorance like that.
Personally, I have 4 easy to load horses, but one of them tries to back out upon getting loaded, so I need a 2nd person to shut the back gate immediately when she gets in - I would have no other way out of the trailer if it wasn't for the escape door.... now, she's a sweet horse, and wouldn't harm me, but if a horse like that were to panic, I wouldn't want to be trying to sneak past them to get out the back.