I'm not an expert on this topic, nor well read or experienced on the topic of being an alpha male... but from what I understand about our inner child, is that it's basically all of our experiences, thoughts, feelings, emotions, and "imprints" we had as a child. This is a really good link I found while researching more about it from this thread:
http://www.crystalinks.com/innerchild.html
I'm not exactly sure if one can "kill" it or if it will ever go away, but from what i've experienced with my own inner child, is that it needs to be loved. I would most definitely be classified as the "Spoiled Child", lol. I've noticed that all my negative thoughts and emotions tend to stem from that root. There is this voice in my head that is always looking for attention and wanting to do things for attention. If I don't get it, I usually end up pissed off at the world and everyone in it, or i'll go and sulk in a corner til the experience passes. It's a really selfish aspect of myself but i'm slowly becoming more and more consciously aware of it. Before, like say when I was a child, I was completely unaware of it. Now that i'm older, it's becoming more of a choice. I can choose whether or not I want to give in to it's selfish demands, or simply see it for what it is. A part of myself that wants to be love and accepted. It's also because of it, I realize that it's more important, and even satisfying, to do things for the unconditional benefit of other people rather than personal recognition, attention, etc.
It's different for everyone though. For some, they suppress their "Playful Child" and instead only focus on work, work, work, work, work. They leave no time for rest or relaxation. I wouldn't doubt their inner child is constantly asking them to just let it all go for a while and make time to play. I don't think the inner child is all negative though. I'm sure some people still have their inner child intact and infused with their adult selves. Take Einstein for example. He was like an adult child genius. He said that all his insights came through intuition and a playful sense of wonder. The same went for Nikola Tesla and Sir Issac Newton. I don't think it's only limited to scientists or physicists, but to be an innovator in that field, or anything in life really, you need to keep yourself open to the infinite wondrous possibilities of the Universe. As children, we weren't really concerned with the "answers" to our life situations. We kind of just were. Going along with the flow. Doing our own thing. It's not until we became older and developed our "ego" or social mask/identity, that we tended to suppress or ignore that inner child within us for the sake of maintaining the status quo.
Even through those "rites of passages" (especially losing your virginity), people can still have their inner child running rampant within them. Sometimes even more so. Especially in modern day society with the whole emphasis being on sex, sex, sex; children themselves are losing their virginity without really having the mental/emotional maturity to truly understand it. It may be the action of the "Abandoned Child" looking for love and acceptance and thinking they'll find it through having sex with someone else. It usually only tends to dig themselves deeper into that aspect of themselves though. Which most likely isn't very good. All of those rites of passages are meant to be symbolic, but each and every person comes into their own individual maturity in their own time. Which in essence, is the true meaning of being an "Alpha Male" in my opinion. I believe that AM only helps to influence and enhance the process of that maturity.
Einstein was an alpha male in his own right. So is Johnny Knoxville too in a way. The same goes for Shakespeare, Leonardo da Vinci, Abraham Lincoln, etc. I think it's only when we learn to truly become aware of our inner child's needs, and develop the wisdom and understanding to provide it to them, whether in the form of unconditional love, acceptance, attention, fun, etc... that we will become the matured individual men/women we aspire to be.