If the problem is not that you can't live, but that you can't live officially, I would say that is still a problem.
The wages payable are still at the mercy of what the market will bear. If these people could not find a way to live officially, in many cases it's highly unlikely that the wage could rise to cover their cost of living and the taxes to be paid, meaning the job would no longer exist.
At the end of the day, you can't tax a society into prosperity. Every tax dollar spent needs to be justified on an ROI for society.