This is the standard in the Scandinavian social democracies. They have no minimum wage laws (though unions supplement that greatly) and a competitive labor market pushes wages up.
Much like housing, the best solution usually isn't government price controls. Better (if feasible) is abundance in the market.
Why are tech wages lower in Scandinavian countries than in the United States?
We don't need a minimum wage if your minimum needs are met.
When everyone is the same (genetics, background, culture, etc) there is very little structural inequality in a competitive market. In an empire like the US, so many groups exist in a hierarchy that government support is required. In such an environment bare competition simply reveals and highlights fundamental difference, which is not conducive to social cohesion or harmony.
They also have a much better safety net. Healthcare not being tied to employment is already massive.
I think a flat tax + UBI is the only way to go. The dream of AI should be a society where maybe 10% of people have to work. The nightmare is if the other 90% still need work but can’t find it.