It's weird - with horses, I would always be careful to keep the jumps lower in practice, but I hear a lot of agility people say that their dog has trouble adjusting to various heights, and that changing the heights can throw them off. I don't know if it's just habit and muscle memory like Dekka mentioned, but it was something that surprised me.
Suzanne Clothier's jumping program was actually inspired by watching and studying horses jumping, so I do think there's a pretty safe comparison between horses and dogs.
From reading her book, I think there is muscle memory involved and also "smart jumping" involved. Muscle memory can be bad, like in Auggie's case where he developed a habit of stutter-stepping no matter the jump height, but it can also be good - hence why about half her program is a series of five jumps set at two stride-lengths apart, and then oxers set at two stride-lengths apart. Dogs get into a nice rhythm and it completely broke Auggie of his stutter-stepping because he learned instead to just have a nice, steady, even pace (and the oxers teach them how to properly sail over bars and clear jumps.)
But then the other half of the program is teaching dogs to be thinking jumpers. This is really important IMO for agility dogs since they HAVE to be able to think on their feet.
And I can only speak for Auggie and say that when he has been used to 12 inches in practice, 16 at a trial is too much for him. He can still jump them, he can clear bars, it's not a physical thing. Our NAJ we got running 16. But mentally it seems to be too much to make that sudden switch up AND have everything else going on. If you set the bars at 16 and ran him through a straight jumping chute, that might be different... it's the combined trialing factor, IMHO, not just the height of the jumps alone.
Then again, Auggie is pretty young and certainly early in his agility career, so as he gets more seasoned when it comes to trialing things might change. I think there's a LOT involved there. It is definitely a mental strain of running a course, not a physical strain to get over the jump or a problem judging the height of the jump.
Buuut I think I would still prefer to mainly practice jump him at the same height he is running in order to keep him largely conditioned to that... I'm not sure. It's definitely an interesting question and something to think about.
JMO and from my own experience - other people might have totally different situations with their dogs!