Why do most GA aircraft not have vortex generators? It is my understanding that vortex generators produce more favorable aerodynamics by delaying flow separation. If this is the case, why do more GA aircraft not have vortex generators?
Vortex generators are a kludge - a good design does not need them.

They are mostly added at later stages of the design process when some deficiencies need to be cured, but re-designing the aircraft is too expensive. They add a lot of drag, and do so always, for the whole duration of a flight, when they are needed only in some corner of the flight envelope (say, when flying close to stall).

A clever way to install vortex generators can be found on the Short Belfast:



Tail of the Short Belfast from below (own work). Note the vortex generators hidden in the hinge gap - they only move out into the airflow when they are needed: When the elevator is moved to large negative deflections.