If I may, I do think a bit more rigor is possible.

"Democracy" refers to ‘a democratic political process’. That means all citizens have freedom of political speech and there is a recognition that any restriction on any other form of participation in the process (running for office, voting, peaceably assembling, and petitioning the government) must be 'democratic' in nature: it must be universally applicable and universally applied.

That makes it non-arbitrary, therefore just. (Locke correctly recognized that arbitrariness in human relations is injustice; I have never seen anyone even attempt to contradict him in that.) That makes being democratic the only just form a political process can take. That makes it, for people who care about justice, the only ‘good’ form a political process can have.

We have learned over the centuries that age is the only undebatable restriction of that kind. It is a proxy for emotional and intellectual maturity. Creed, property, 'race' (color of skin), and gender have been ditched as restrictions because they obviously violate that principle. Any of us could become a felon or lose our fingernail hold on reality (two other restrictions that do exist), but those restrictions are clearly not as purely non-arbitrary as age is.

Should anyone reading this be curious for more: "Democracy: So Much More Than Majority Rule" (here in Medium but not behind the paywall).