That's only part of the equation though.

If lower income means you qualify for subsidized housing, subsidized childcare, etc then that can be a big incentive.

I have two sisters with very similar lifestyles despite grossly different incomes. My low-income sister gets her housing, groceries, utilities, childcare and even phone paid for by government programs. My other sister (near median income) lives in an apartment of similar size and quality, buys similar groceries, etc but pays for all of it from her wages.

My low-income sister has no real incentive to increase her official income (although she does value informal economy "hustles" and side-gigs which directly give her disposable income).