I don't see an actual shortage as such, but there doesn't seem to be the glut of FI(R)s knocking about looking for a first job either, that there was a while ago.
While having instructors as self-employed contractors, is on balance largely because it's advantageous for the club, it's not totally one-sided. As a freelance you will end up paying less tax and NI than you would as an employee, although you do sacrifice employment protection, paid holidays, NMW & working time reg's. If all FIs were employees, you would find that either the price of training flights would increase to cover employment costs and/or employed FIs would end up on salaries of somewhere near NMW levels. Although some may say that's not far off where they are now. I've been self-employed all the time I've worked for someone else since I got my AFI rating, it's worked just fine for me, but then I've always been PT with another source of income, I concede I may think differently if I was trying to live off it.
schools would have to start offering a decent wage to PPL instructors
Sorry, but I've been hearing that from generations of instructors for decades. It's just never happened, everybody was sure it would when the BCPL came in, due to the increased costs of becoming an instructor, again whenever a pilot shortage loomed, but it didn't. Unfortunately, the market just won't seem to support a charge of £50 per hour for the instructor, which is about what it would need to be to pay an employed, salaried instructor about mid-twenties £k a year, which isn't actually that much.