True. Also, there are definitely traditions and notions about better and worse jobs which play a role, besides supply and demand.
In some countries salaries for some jobs do not rise even though there is a clear lack of supply. But they just cannot move the salaries up (by much), for not disturbing their artificial salary hierarchy. You cannot pay the nurse better than the physician, even if you are direly lacking nurses and have a surplus on the physician side. Well, you could, but nobody actually does it.
This is often because they are a monopoly and their pay is artificially restricted such as by having only one employer