For JC Racinet, the dominant use of medium trot is one of the aberration of modern training.
Indeed, too many people consider the medium trot to be the normal trot their horse should give them. But before asking your horse to go in a big trot, you should make sure he is using his back properly.
Especially with young horses, this is a difficult gait. The horse has already to use a lot of energy upward, to get his topline to sustain his whole body and your weight. The more muscled he'll get, the more energy he'll have at his disposal, "stored" under your seat. It's only when you feel that you have enough gas under the saddle that you can ask a bigger trot.
If too early, you ask the medium trot as you're asking your horse to raise his back, then you'd be asking for two different and difficult things at the same time : the lengtening of the trot and fastening of the rythm - forward energy and the raising of the back - upward energy. And because it's more easy and urging to give in to the leg order, the horse will hollow his back and rush forward. You'll get the medium trot but you'll lose the back.
The impulsion is not something you ask, it is something you gather, a situation you create.
And it takes some time until your horse is feeling as confortable and powerful in his trot so that you feel you have extra energy to use in a bigger trot.