Expanded EITC is good, AND raising the floor is good too.
The appeal for policy makers is that there are no direct taxes.
Odd, though. One thing embedded in your argument is the implicit argument that young people don’t deserve to be paid a fair wage. Federal minimums have been stuck for a decade, and in states where there are more progressive cities, the legislatures have worked to inhibit local minimums. People do live and work not just at the minimum, but at wages where that is the defined floor. Raising the standard ends up boosting wages near the floor. There’s a lot of research on this out there, and not just one professor’s opinion.