Your right, and your wrong about an alpha male. Most PUA systems I have read talk about an alpha male in a godlike sense. I don't know about you, but I am not naturally the type of person who wants to be in charge of, or try to lead large social circles. I only have so much social energy and I don't want to waste it all to try to stay on top of a social group.
Being at the top of a social group will help you get results with women, but it generally takes a lot of work. If it doesn't, it means that the group is a relatively low value group, and it hurts you anyway.
Here are the key qualities of an alpha male, in my experience:
1. Assertive when he needs to be
2. Does not accept other peoples' frames of reference.
3. Has fun regardless of the groups problems and sentiments.
4. Does what he wants to do.
Some things to note about these items:
You may not be the most dominant man in the group, but you still won't have any problem getting women. You don't have to be weighed down by the groups demands. In a sense, you transcend the needs of the group. Also, you will often find that you will naturally lead the group because you are having fun and doing what you want to do. Everyone wants to have fun, so if your the guy having fun, they will follow you. Since you are not actually leading them, you have no responsibility for their needs, and they cannot get angry at you for attempting to lead them anywhere.
One of the biggest fallacies of the Alpha male, is that you must always be the top dog of a group. If that is your aim, you will be socially drained and often come off as insecure about your position. It is far better to be the alpha male that I have described, and be able to come through in the clutch, when someone needs to make a decision.
Related story:
The other night a friend and I were hanging out with a cute girl. It happened impromptu, and he knew this girl from before. It was clear that he was the more dominant male in our interactions with each other. However, I wouldn't allow myself to be unreasonably dominated. When he would attempt to make fun of me or be overly assertive about the girl, I would joke it off or ignore this frame of reference that he attempted to thrust upon me. At the end of the evening, I was the one who got the girl, and yet, he still held the technically dominant position of group. I just played normal game, and refused to allow myself to be pigeon holed in the group dynamic. That is how the true Alpha Man works.