However the fact is that if you really want to know how well trained a horse is ask them to do something that requires some real work like working cattle. You will find the holes in your training real fast.
Come ride one of my horses. You will soon learn what it is like to ride a well bred well trained horse. No robot here. That would imply that you have to do nothing in order to ride them. Not so. If you do not know what you are doing you will never get them to move. Neighbor girl found that out a few years ago. She started out riding my stallion. He will pack anyone around. Yet put someone who knows what they are doing and you can go out and do anything with him from reining to cow work to roping. Now same kid on my Dun It mare. She is not a packer. You better know what you are doing and know how to cue her or she will not move. Not one muscles not one inch.
Even if we too have very well trained and very well breed horses and we have them jump over 1.50m obstacle instated of cow work. Or do Haute Ecole and you too could be very surprised while riding them!