So, is 21 the right age? Is 18? Is 16?
Honest question: how would you go about answering your question?
Economists disagree with each other, so it's not something that an HN comment is going to resolve.
Me, I based it on how the minimum wage from the 1950s, adjusted for productivity, would be about $25/hour - https://edition.cnn.com/2021/02/21/politics/minimum-wage-inf... .
This means the productivity benefits are going somewhere, but not to the poorest people who are working the most.
Raise minimum wage to $20/hour (and/or increase collective barganining power), and raise taxes on the wealthiest, and increase the social safety net - pretty bog-standard social democratic viewpoints.
That is, I believe there's a big thumb already lowering wages to below its worth. So the real question is, how do we determine "worth"?
Some countries with strong unions, like Denmark, have an equivalent of $20/hour minimum wage for McDonald's employees, even though Denmark has no minimum wage.