Doodoo, Sorry but I'm speaking from direct experience dealing with manufacturers and other employers as part of a State Government.
It's not only the airline industry that whines about shortages - all industries do, but they conveniently always leave out the second phrase of their whine to whit:
"I can't find enough skilled people to work for me, at the wages I want to pay them!"
I'm afraid you have forgotten about the large numbers of pilots who have left the industry completely. There is no need to import foreign labor. it's the same in almost all industries I can think of - the plumber/electrician/toolmaker/nurse/policeman/welder/LAME who are now running their own shop or lawn mowing business after getting fed up with wages and conditions - thats where the common wisdom about changing careers four or five times comes from.
For example, my first degree is in engineering, but do I want to go back to designing tooling for annealing cartridge cases as I once did? Nope. The hours and pay were crap, but I still could, if push came to shove, and someone offered me $250K per annum.