Military service wasn't mandatory in Starship Troopers, but only those who had served could vote. I'd actually be willing to consider a system like that, but a mandatory draft is by definition involuntary servitude.
"We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.--That to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed..."
Consent of the governed is required for any government to be legitimate.
Our government has no legitimate authority to make us purchase, through military service, our sovereign right to give consent in the form of the vote.
Our rights are endowed by our Creator. They are not privileges to be granted by "our masters" at any price, including military service.