The issue though is once you raise the wage of said people the market readjust the value of other things and puts said people back in the same position they started from. This loop causes inflation and further widens the gap that currently exist.

Social programs function similarly in manner because they were meant as measures to offset the difference but due to how poorly written they were/are being used as a primary method instead of an additional aspect. If raising the minimum wage fixed the problem it was already tried and didn't work. Why would you keep trying the same failed solution despite all evidence showing it doesn't work?