Bullshit. I have the skills for an intermediate-level data engineer, but I find it bland and I'd rather work in computer vision. However, offer me enough and I may reconsider, and I don't think I'm alone in this.
I basically wrote the same thing as a reply to your sibling comment. Data engineering would have to pay a lot more than I currently make for it to be an option, and even then I'd probably change fields once I paid off my student loans and saved some money.
But the pool of people who wouldn't otherwise take the job grows as the salary increases, pulling the people away from careers where they clearly aren't providing as much value to their employers.
Put it this way, the company isn't going to pay the employee more than the value they provide. That is the ceiling on salary. So until that ceiling is reached it is indeed a case of higher bidder takes all, as your thought experiment demonstrated. But once that ceiling is neared the company will make the decision not to bid higher, thus reducing the demand.
Thus, there is no shortage, just a shortage to work at the lower salary of companies with lower ceilings, because they aren't capable of leveraging the employee's talents sufficiently to draw from fields with related skill sets.