It really doesn’t matter what minimum wage is set by law. The real minimum wage is zero. That’s what people whose labor is worth less than the legally mandated minimum wage will inevitably earn.
If there must be a legal minimum, and politically that probably is the case, it’s certainly far better to have the level determined by states or even local municipalities. Going by my own state of Pennsylvania, there is quite a variation in prevailing cost of living even within the state. A minimum wage of $15/hr might not do too much harm in Philadelphia, but a much lower wage might be better in the rural central part of the state. No minimum makes the most economic sense, but a flexible minimum set locally would be far less disruptive than a one size fits all federal mandate.
The median wage in our rural area is probably about 10 an hour. A 15 minimum will shut the area down. It’s irrational.