This likely means those consuming the outputs of Mechanical Turk don't have a good way to measure the value (aka quality) of the outputs.
If they did - then they shouldn't care whether it's a human or a LLM. And if it's a LLM - then the cost will roughly correlate to the MIN(cost of the LLM, cost of a human) to do the task.
I think the "state of the art" of measuring the quality of outputs was to send the same task to multiple "agents" and only accept answers if over a certain amount agree. With some human review and reputation scoring sprinkled on top. It was a while since I was in this field though