I see your point, and thinking about it helped clarify my thinking, so first, thank you for that. I think another way of phrasing my opinion is that the US labor market is a large, reasonably efficient market; that it's reasonably well modeled by a simple supply and demand model; and that discussing it in other terms obscures the important issues. The notion of a shortage is fundamentally incompatible with a simple supply and demand model of a market. The market price in such a model is, by definition, the price at which supply and demand are balanced. So if you're talking about a shortage in the US labor market, you're either claiming that supply and demand is a poor model of the labor market, or you're talking nonsense. I think either is misleading or at best confusing. So to an extent I really am saying that shortages can't exist for anything you can buy on a large efficient market.

Of course not every market is a large efficient market. If you're talking about a price-regulated market, by all means, discuss shortages. Another good situation where discussing a shortage would be appropriate is markets that have very or perfectly inelastic supply over a relevant time period. Say, a vaccine that costs $1 but that takes 6 months to produce due to the biology involved, combined with a major epidemic in the relevant disease. It's fair to call that a shortage.