"Due to the nature of poor people having no economic option except to do labor, the above system would effectively only return the money back to the workers."
Which would then mean they could command more of their own output in competition with the rich and therefore not have to work Friday. The rich would then have to hire those currently without work to do the Friday shift, and those that don't want to work would have to work the Friday shift if they want to eat.
All of which is perfectly fair and reasonable on a quid pro quo basis.
What you want to do is force the current workers to work Friday for nothing, then take that output and give it to even more people who don't want to work for a living - adding to the existing rich who are currently doing that.
That's doubly unfair on the workers.
To stop that unfair extraction we need guaranteed jobs, not guaranteed income.