> Do people who are paid 10x necessarily consume 10x over a person paid minimum wage?
Even if their consumption was 1x, my point would still stand. Most people aren't earning minimum wage, nor are their salaries affected by minimum wage increases. This means that the cost of most products does not increase as minimum wages increase.
Minimum wage increase money comes from somewhere, and since ~everyone relies on minimum wage workers, that means that ~everyone pays for that wage increase.
If you take a dollar away from 100 people, and split half the resulting money between the 10 poorest in that group, and the other half between the next 20, it's a regressive tax, with a progressive benefit that has a net benefit for the poorest. Minimum wage increases work the same way. The rich lose very little, the middle class lose some, the poor win.
Are there better ways of structuring this sort of thing? Theretically yes, but practically, the rich are really, really good at protecting themselves from wealth redistribution. If you're going to hold the poor hostage to them, you're never going to get anything done.