Price controls force efficiency gains. If wages go up you don't stop paying your employee wages, you either train cheaper employees, find a way to get more work out of them, or find a better way to do it. The same applies to price controls.
This is not true. The moment you set a red line, you're making impossible for the lesser trained to join the wagon for getting a chance to climb the ladder. Also, you're making the capitalist not paying for not hiring lesser people, since none has to hire, there are not faults. The idea is that investors should fight to get you in, but if they're denied, they get the monopoly since no one can enter the market to compete with them by hiring people who is willing to work for less than the regulated wage price is meant is. Plus, wages will not go up easily, since you're killing the force supply by setting a line on it. Milton Friedman explained this properly, you can see his speech on Youtube.
Milton Friedman is only one school of economic thought. Nothing is proven in economics and likely won't be since it involves human psychology. When gas prices rose dramatically economists expected the US to move away from large vehicles. That's not what happened. The rational thought is almost never what happens in economics. People buy high and sell low, their purchases are often emotional, and investors pour money into acting blockchain.