I understand your position, and I don't think your definition of "shortage" here is unreasonable. But shortage is a relative term--"short" relative to what?--and by some measures, there are real shortages in these situations. If we use corn instead of labor, for example, we might have a bad harvest one year, and the price of corn goes so high that it's not worth buying for certain products. The market still clamors for those products but isn't willing to pay what they would have to pay given the new price of corn. Your definition, if I understand it, would say that there is no shortage of corn; it's just more expensive than you can pay.
I'd still call it a shortage of corn, because I'm thinking of it relative to previous years, future expectations, the causes of the price change, etc. Rent control or earthquakes cause what many would consider a housing shortage, gov't price controls or bad weather create commodity shortages, and sufficiently generous welfare programs (you have to pay a lot more to make it worth working at all) or explosive increases in customer demand (not enough time for labor to learn new skills) can create labor shortages.
From the perspective of an employer, no longer being able to hire people at a wage that makes them worth hiring can be seen as a labor shortage, while from the perspective of a worker, no longer being able to get a job at a wage worth working for can be seen as a jobs shortage, but I agree with you that, especially if the changes are just the long-term evolution of the economy, there comes a point where it no longer makes sense to refer to something that will never come back as a "shortage".