The word "Alpha" gets used around horses a lot and means something different to each person.
You can have a horse that is dominate over the other horses and it does not mean that the horse is a leader.
The horse can just be a bully and not really a leader at all or is just a bad leader.
The combination of the herd can put stress on the other horses and this is not always good.
It has been my experience that many horses are not good leaders at all and are just in the position of being on top with no skill to actually lead.
I have a mare here that is truly a leader and is NEVER challenged by anyone at all.
The seas part as she walks calmly through the herd.
There is no violence and everyone knows their place.
Wherever she is placed order is restored and the herd is calm.
The order of a "balanced domestic"group of horses can be deeply and drastically upset by a junior bully's and this in turn can effect the harmony of the other horses and also effect their sense of well being.
I have seen many behavior problems come from bully's beating up on a more submissive horse and that horse becomes defensive and mean.