You're making the error of deducing market conditions from price (or price from market conditions).

Market price is determined (in a well-functioning market) by the intersection of supply and demand. So the salary could go other way: higher, if a non-compete makes it harder for the employer to find employees willing to sign the clause, lower, if result is fewer alternatives and/or more desperate employees interested in the position.

I'd actually argue the second: that noncompetes raise employees' switching costs, and reduce their alternatives, so that a state in which noncompetes are valid and widely applied would tend to have depressed labor rates.

No; in a good market the employer who wants a non-compete would need to pay me up front for the time period that I wouldn’t be able to work after leaving her firm, plus a premium for the expected difference between my salary at that point and my salary at hiring, which would make the wage for positions with a non-compete significantly higher than those without.