If I "need" to work to support me and/or my family, then a company is going "coerce" me into accepting the lower wages. That doesn't make me "willing" that just makes me desperate. And, as was shown in the last century.... companies were shown to be manipulating the system to drive wages into the basement. They couldn't be trusted to pay a fair wage, so society enacted the minimum wage laws.
Companies were also using this leverage to make people "willing" to accept wage cuts even after being hired, with the threat of being fired if they didn't match the wage that someone else might be "willing " to accept.
By your logic, if you are renting an apartment, then you could be evicted by the landlord if someone came along and was "willing" to pay just $10 a month more. Unless you were "willing" to pay at least as much as they were.
That would be a interesting system. Each month you would have to go to an auction and 'bid' how much you would be 'willing' to pay to stay in your home. As a landlord I'd love that. And I'm sure I'd never ever do anything to keep the prices up, like hire a shill....