The solutions are suggested in the problems. Don't let the union control the entire profession. The AMA's (legislated, btw) stranglehold on the medical profession is limiting entry into the field, which in turn creates a scarcity of medical professionals, which in turn increases the rates they can charge. Open the market, and that problem goes away.
This sounds like a regulatory mechanism. Who should enforce it? The government? In that sense I agree - someone needs to watch the market and (re-)establish balances. But to come back to the topic raised by the OP. What do you do if a majority of your labour force thinks that the wage is too low?