I had similar notions of government and I now work for government. It's important to keep in mind that the upper levels of power in these organizations tend to be handed off to people in similar class and standing. Most army leaders for example were part of the upper-middle to upper class in the first place. They either arrived in the corps with specialized training or they got it via the corps and attained a higher standing. They weren't grunts.
If you want to change the organization from the inside, it will be next to impossible. Its structure is self-perpetuating. You would have to change congress and their power is also concentrated in the aristocracy. Once you realize that democracy is a joke and the choices we vote on are created by the aristocracy, you'll see that nothing truly changes.
If you want to join the corps, do it because you want to serve your country. If it's to change things, you will likely just end up being changed instead.