The disengagement of hindquarters seems to be a staple of most of the ground work schools, not just Parelli. It immobilizes the horse by making him throw all his weight on the forehand.
I don’t want my horse to stop by falling on the forehand.
I want the horse to move the hindquarters by being engaged behind, that is to do lateral moves with lightness up front.
The result is that these days even if I try to disengage the hindquarters when maresy is a bit fresh in hand, what i get is lovely shoulder in on a circle, and moments of passage. Or a super collected canter in hand on a ten meter circle. These don’t unfortunately translate to work under saddle, but she is now very athletic on the rare moments she acts up in hand.
I assume disengage the hindquarters is a way to get green or unbalanced or downhill horses to slew around and not be able to move. But it isn’t something I’d want to emphasize, and it isn’t something that is in fact effective once the horse has learned to move the hind quarters while being engaged.
And for me, anything you do on the ground has to contribute to better work under saddle, not detract from it. Has to build desirable skills from the get-go.
I train a lot of lateral work in hand, but not in the NH way.