so that the politicians who send other people's children off to fight also have to send their own.

Right, because politicians always follow the same rules we do and totally wouldn't just find a way to dodge the draft.

Most soldiers in a "professional" army are there because their families are poor and they have few other options to make a living.

You're right. Many feel forced into it by unlivable economic conditions. That doesn't mean we should answer wage slavery with more slavery.