It's central to their societies philosophy that the people with the ability to influence the government have the understanding and commitment needed to actually contribute positively.
They will actively try to discourage people from joining by showing the horrible shit that can happen to you in combat specifically to weed out people that aren't actually committed to the understanding that service is supposed to instill in you, and people are free to leave service at any time, for any reason, with no punishment or ire from the government or society at large. You just say you want to go home, and you can go home. The only thing that changes is you can't re-apply for service, you only get the one chance.
It MUST be your choice to serve. Conscripting people would destroy the entire point.
Before the Federation, the Earth was fucked. Global wars destroyed everything, gangs roamed and pillaged as they pleased, and there were no governments left. Millions of combat veterans that bled and suffered for their homelands were left with nothing to go back to and nothing to show for their sacrifices. They were the ones that formed the Federation, and they were the only ones that truly understood what the Federation could give and why it and the ideals behind it needed to exist.
Voting is not simply a... reward for service, it's a responsibility given to the people who truly understand what it means. Being a citizen is a sacrifice.