That does not follow. There are many cases where the total demand exceeds the total supply; in such cases, no amount of "paying more" will alleviate the shortag

That does not follow. There are many cases where the total demand exceeds the total supply; in such cases, no amount of "paying more" will alleviate the shortage, you are just moving it around. Furthermore, the upper bound on pay is the amount of value that can be generated with those skills -- a market requires buyers which requires a positive exchange for both parties. Consequently, the market clearing wage in a skill shortage is a function of the amount of value a company can create with a given set of skills. The challenge for highly skilled labor is that the latency between a market demand signal and new supply is typically many years. Demand won't manufacture that supply on any time horizon that matters.