Hmmm interesting that you've found they need too much leg and hand! I use barely any, of course as with anything, the greener horses will need a stronger aid than a more experienced horse, until you can fine tune the aids down to barely perceptible shifts in weight. The mare I'm competing at the moment is ridden purely off seat, I don't need to touch her with my leg for upwards transitions, usually the only time I'll apply leg is to get a little more activity or elevation in her paces, and even then it is a light bump with my calf to get the desired result. As for the mouth, put someone heavy handed that will grab at her mouth on her back, and she will cart them around like a giraffe! Put a rider than knows how to engage their core to use an effective seat on her back, and she goes like a lamb, will turn just by moving your shoulders slightly, stop by weighting your seat slightly etc.
It saddens me that you've only had the chance to ride horses that may have been trained in this 'modern' way of jamming the head in to make flashy front ends by with no hind end, that's what results in a dead sided, dead mouthed horse.