On what basis is it good for a large segment of the workforce to make a below livable wage?
People make the mistake of conflating "minimum wage" and "liveable wage."
I worked in fast food for years while I was in college. The employees generally consisted of high-school kids and college students, and mothers earning supplemental income. NOBODY outside of management considered their jobs career, and NOBODY thought they were earning a livable wage. EVERYBODY knew it was spending money on the side or supplemental income. The concept of a minimum wage being a livable wage is a idea that was recently created.
Are thriving/ flourishing areas areas where the majority of residents earn low pay or high pay?
My main work area is in an interesting example. It's a high pay area, as the money is coming from Wall Street, investors, etc. Minimum wage isn't even a consideration for anything. Maybe some high school kids at mom and pop shops are being paid that, but nobody else is. Increasing the minimum wage won't really do anything, other than if the wage floor is raised elsewhere, it will also be raised here.
The market dictates the prices. I don't know the only McDonalds in the area is paying now, but they were pay $10 plus benefits 20 years ago, because they could not attract workers for less than that. I wouldn't be surprised if it is nearly double that now, due to the overall pay increases across the board for the overall service industry. But this much higher than minimum wage/significant wage increases hasn't really changed anything. The people at the bottom are still struggling, their purchase power in the area hasn't increased, etc. as expected.
If more workers getting higher pay in a depressed area results in them spending the $ in local areas /patronizing other businesses there, what might that mean for an area?
Plenty of examples of that everywhere for all time. Workers make more money, and the prices of everything increase, as expected. I don't every think I've seen an example of simply paying people more money makes them richer; i.e., they have more money, everything else in the market remains static.