> Further, it can only happen if the unemployed person qualifies for the maximum benefit in their state, which the vast majority of unemployed people do not.

This is backwards. The lower the income the greater the relative benefit from the fixed $600 assistance since as a rule of thumb unemployment pays a little over half of the replacement wage.

The simple solution would be for the government to also pay employed low-wage workers. Then, everyone can continue to buy food and pay rent and no one is earning less while working.