"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.
In theory I agree. The problem is that our "democracy" increasingly involves people voting to forcibly take the property of their neighbors for themselves. I can envision a system of weighted voting. For example, every citizen gets one vote. Those in the military or who have previously served get another vote. Those who are net producers (i.e. pay more in taxes than they receive in benefits) get another. Entirely impractical, but it's interesting to consider. (Of course none of this would be an issue if our government would respect the Constitution, but that's even more unlikely).