There are 6 things that affect collection which is what you are along towards when you talk of hind quarter engagement I presume.(ignoring conformation)
3) Connection (rather than disconnection)
4) Perception (the horse has to be allowed to feel what collection is so it selects that option normally)
6) The Rider
Balance and flexion are commonly skipped over, or at least it's forced (for example by riding circles you develop flexion will be one answer which is actual not the best way) Forced flexion will not lead to natural flexibility and balance. It always results in stiffness somewhere else.
Of all of these the rider is the biggest hindrance. All too often we look at the horse as failing when it's commonly the rider. They are unbalanced, unfit, stiff, incorrect position, braced etc etc etc
Perception is probably totally ignored in general. Few horses I see are helped to understand what we are trying to achieve. Instead they are pushed and pulled into a shape in the hope that they will eventually hold it from choice. If the horse gets to feel real collection, engagement and its power then it can understand what we want and why it is good. Then it is much more likely work with us.
The biggest issue as always however is the rider. Few of us (myself included) have the symmetry, core strength, stability, flexibility and neutral posture to really work with the horse and not against him. Yet how many of us actually take time to do our own core exercises and stretches to improve our performance before we get on a horse?