Doesn't supply and demand dictate that keeping population constant and limiting career options will lead to an increase in supply in the still available career

Doesn't supply and demand dictate that keeping population constant and limiting career options will lead to an increase in supply in the still available career paths? This will either be met by a decline in real wages or, if real wages can't adapt due to regulations, an increase in unemployment in those fields? This seems a lot like trying to cure a symptom without understanding the actual sickness.