Piecework (and Mechnical Turk!) probably makes more sense in an environment with Basic Income. That gives the employee a chance to decide if the effort is worth the $/piece without compromising on their health and welfare.
Monetary supply/demand is a tiny bit more complicated than that.
This isn't a downside of basic income, there is always a floor on the amount you can pay for labour. If you pay below what the market expects you are only going to get the truly inept to do it.