Marvin Miller, Free Agency, and Say's Law

In Eric McErlain's excellent postings about the NHL/NHLPA settlement, he mentions Marvin Miller, the first successful leader of the Major League Baseball Players' Association.

Marvin Miller, the godfather of MLB's labor movement, noted that the most important concession he got from owners was to structure the league so only a limited number of players would become free agents every season, thereby boosting their value.

I remember having read this several places and having been puzzled by it. When a player becomes a free agent, that increases both the supply and demand, not just the supply. The team that loses the player will also be looking for a replacement. Furthermore, teams that are looking for a free agent will be doing so, typically, because they have freed up a spot. I know there are variations, but typically an increase in supply will also mean an increase in demand (and vice versa). Both curves shift outward, and there is no particular reason to expect the equilibrium price to change, on average.

More trade doesn't necessarily mean lower prices, and thin markets do not necessarily mean there will be higher prices. What if the players who become free agents in a thin market have skills that not many teams want? Then a thin market might just as easily lead to lower, not higher, salary offers.

Isn't this just another application of Say's Law?