The damage is normally due to sudden “loading” of one or more limbs as they try to stand up when not fully coordinated. The easiest way to break a bone in any species is to load it under torsion.
Restraints would have to be so strong that they could in themselves cause damage…there is no way of attaching them that would be safe, horses muscles are incredibly strong….what sometimes happens is that one or more ropes are attached , with very experienced people on them, who try to counteract the “stagger” as they get up…but that is potentially very dangerous to the people with half a ton or more of uncoordinated horse.
The problem with additional sedation, is that not only would the effects be unpredictable, but they could make the uncoordination worse.
Essentially horses tend to go from semi comatose to wanting to be on their feet and gone in seconds. Many combinations of drugs and physical assistance have been tried over the years, but there is no fail safe method.