This mischaracterizes a more complex situation and conflates several things. While simple unwillingness to pay a market clearing price is the cause in some cases, I would assert it is a small minority of cases in practice. Some other important causes of labor shortages:
- Labor intensive, low margin industries typically have long-term financial structures that don't allow for high wage volatility. Most workers also dislike wage volatility, so this arrangement works. However, this means that there is limited ability by the business to address labor shortages by increasing wages.
- There is an actual labor shortage. If the market needs 1,000 neurosurgeons and there are only 800 in the world, no wage level will make that shortage disappear and it may be many years before the market can adapt. This is painfully evident at the high-end of the software engineering market. Paying higher wages doesn't eliminate the shortage, it just moves it around.
- Individual wages are capped by value produced. Companies that can pay the highest wages are those where employees produce the most value. The value produced by employees is finite so at some wage they are effectively unemployable; the market has to clear in the other direction as well.
- Spatiotemporal latency and distribution i.e. the required skills are trainable but do not exist when and where you need them. This is increasingly challenging as businesses are required to adapt on shorter timeframes; human populations change and migrate at relatively slow rates.
- Local monopsony for labor sets an economically optimal clearing price for the buyer. This creates a synthetic "labor shortage" of sorts in company towns and similar; market clearing, but in a skewed market. This is not the situation for the vast majority of Americans.
Most labor markets are some combination of all these, and the first four reasons are common in most American labor markets. None of those real labor shortages can be reasonably addressed simply by "paying more". That isn't how markets work.