1) Horses can be easily trained to obey / run off and come back using verbal / other commands - fact and realistic
2) Stallions can be trained just as well, however it usually takes longer / more difficult. I won't bother going into the mechanics, but usually due to such training, the stallion is likely to become a one-man horse (ie. will only see the trainer as his master). This once again greatly depends on an individual's horses temperament, since you could enconter very similar problems with mares / geldings during training (although rightfully said, it would be less likely)
3) Horses (stallions / geldings / mares ) in general, could develop a natural response to defend the person on their backs by any means nessesary, although this is rare in today's world, because everyone associated with horses spends a lot less time with them, only think about horses as sport, and sell / buy several horses in a few years. It is true however, that this type of a 'bond' will occur faster with stallions, since it is a part of their natural herd behaviour.
4) Horses are a lot more intelligent than people assume. In other words, a stallion would not go after a mare during a battle, or under any other circumstances if trained correctly and/or if he is busy defending himself or his human.
5) Just one more point regarding staying still - although being a combination of all of the above. A horse is likely to remain near his master during such a situation, so infact it would be more likely that the horse would attempt to follow the human he knows during a battle, possibly even trying to defend himself and the human, rather than running away through unfamiliar fighting mess. This obviously can vary slightly on the relationship the horse and rider share, and the training.
Hopefully that evens out most of the arguments. Now for the actual post -
I have no problem with this, except that it would take a while to train a horse to do this. (which brings us back to training horses thread). I would personally suggest the following: Horses can gain experience, with each level providing a 'training point' that you can place in the stats, or save it up for further commands that may require more than 1 point (hence realistically speaking, take time to train).
So for example rearing may cost 5 points, whistling can cost 4 points, while the stats can cost 1 point each etc.
I have updated the
Enhancing Horses thread with this system in the initial post, so its explained further there.