Why should there be a national minimum wage? Cost of living varies so much, it is impossible to derive a figure that is reasonable for the highest cost of living areas and the lowest cost of living areas.

Because there are a number of states that have repeatedly demonstrated that they can't be trusted to make basic, life-improving changes for themselves. Then respectable places like California end up footing the bill when they shake the proverbial can.

A fair number of these states had to be held at gunpoint to eliminate slavery.

Not only is it basically impossible to do a national minimum wage fairly, it is completely antithetical to our system of government. We are a federation of states, not a centralized national government that runs everything else. I wish people would stop trying to make the US something it isn't and was never meant to be.

The states have a lot of leeway in how they run things, the federal government is there to make sure the system stays in some sort of accord.

They do this by offering emergency relief funds for natural disasters, interstate highways for trade and economy, and all manner of things.

I think a federal minimum wage makes sense in this system, ensuring that the people of Tishomingo, Mississippi have the same fundamental buying power as the people to Los Angeles, California instead of them earning $1 an hour because it's comparatively cheaper to live in Tishomingo.

Raising the federal minimum wage is also a good way to decrease old debt, deflate the value of stagnant money (increasing the likelihood that the money moves, improving the economy) and to temporarily boost the financial status of the poorest and most disaffected.

In an age where no one working minimum wage can afford the cheapest 1 bedroom apartment without an extraordinary stroke of luck or some sort of financial dispensation, someone needs to do something and it needs to come from on high.

Not sure where you're getting that idea. Maybe there is some niche case law out there that I'm unaware of, but I can't even think of an example of state law voiding federal law.

The only thing I can think of is the states that have legalized Marijuana. It's federally illegal, but the states simply have chosen to not prosecute.

That being said, if you are pulled over by a federal agent in a legal state, if you meet the federal requirements you can still be prosecuted for possession of marijuana at the felony level, that being said, unless you were doing something super sketchy like having a full pound of weed split into little baggies or something, that is unlikely to stick.