This doesn't seem so helpful to me; it just pushes the question back a step. What counts as "willing" in either case?
This is far from an idle question. When, for instance, I feel thirst, and I get some water, did I just make a willing choice? I certainly would not have gotten the water absent the thirst I felt. Feeling the thirst, I could not long ignore the body's demand for water. So my choice was coerced at least in that sense.
I suspect many people who work menial jobs would, if their choice was unconstrained, demand more for their labor. But, of course, they cannot do so. I recognize, of course, that someone whose job is to sweep floors should not command a hundred dollars an hour or some such lofty wage. But at the same time, people are coerced into taking what labor they can find, and at the wages they can find. I think a case can be made that we're dangerously close to pushing the envelope past its breaking point on this matter, and when that happens, there are going to be some very unpleasant consequences. We're already dealing with some of them.
Adam Smith spends a fair deal of locution talking about this problem. IIRC, it was chapter 8 of book 1 of The Wealth of Nations. He did not believe that wages should be determined by the market, as we was convinced this would lead to a lack of genuine liberty. Unfortunately, not very many people these days have taken time to read his argument.