Why do most 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.