Jumping from trot is something I detested for a long time, and seriously neglected in my horses’ educations.
Then I had a homebred mare who had NO real natural talent off the ground, and I was sternly taught to teach her to jump directly from walk, which was absolutely the making of her (she was called Canoodle, got to 2* and went clear round numerous Intermediates, plus DC at CIC**!)
Most horses won’t need to go back to exercises that are slow and basic, but being able to pop something from trot is a HUGE asset.
Not only is it much much harder for a horse to run out at a skinny from trot (because of the diagonal placement of the hindlegs), which means it is very useful on wobbly baby horses, or when coming to a skinny having already run out at it (!), it is impressive just how big a fence a horse can jump easily from trot, in spite of usually taking off from one hindleg first.
These pics show me and Daisy recently when she popped in a few strides of trot before a pallisade on a mound. This was a new fence for her, hence the few moments of extra thinking-time she decided she needed.
She did not drop behind the leg at all to trot, she kept going forward but just balanced herself a tiny bit more, it’s hard to describe but not a bad feeling at all, you just have to try to keep the leg on and your shoulders up and let them sort it out, by far the best way!
I have jumped very big fences successfully from a stride or two of trot, it is a very useful thing for a horse to know how to do, and can definitely save your necks in an eek moment, in my experience.
Of course if you approach in trot many horses will pop to canter, but it is good to teach them to do it the other way, to pop down to trot from canter without getting behind the leg or hesitating at all.