My only fear is that wouldn't businesses constantly relocate to new areas with lower minimum wages? If the area you're located in goes from $5 to $8 (possibly due to your factory), why not relocate three counties over to an area that's still at $5? A national standard mitigates this issue.
Reloction isn't free either and there are "implcit secondary standards" for the work beyond just the nominal task such as infastructure, literacy, and scale. Even if anyone can put widgets in boxes they may only need very unskilled labor for the task other aspects like "able to read the numbers to know how many to box up" are included. The labor may be technically cheaper across five towns of 200 but a larger factory in a big city could be more efficent because you can muster larger workforces quicker.
A national standard would have merits but more in the sense of scale - it means less friction from adapting to 1 different standard instead of N different standards. It is simpler but has the downside of being low for expensive locales and high for cheap locales and the trade offs that apply to both.
Moving 3 counties means basically every employee has to be relocate or be replaced. If a business is willing and able to make that choice, they are a) not attached to their current location, and b) probably willing to consider farther moves for further cost reductions.
That is already what happens with factories. They find cheap land and cheap labor.
They generally don't move factories unless the wages are enough different to justify all the other pain and expenses that moving would entail, including hiring almost all of their low-pay workers from scratch in the new area.
