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?
The vortex generators are used in commercial aircraft (Boeing especially), for a number of reasons, which are usually not applicable to GA aircraft. For example, vortex generators are used for anything from stall alleviation to vibration reduction to noise reduction, some of which are not applicable for GA aircraft. Also, they are usually added during testing, which is much more expansive compared to the GA aircraft.
That said, vortex generators are found in some aircraft, like the Piper Malibu Meridian, as shown below, because of their advantages.
Image from www.nasa.gov
Another point is the a number of companies offer retrofit of VGs for GA aircraft. A number of GA aircraft have been retrofitted with them.
By Ahunt at English Wikipedia - I took this photo and release it to the public domain, Public Domain
However, they are quite costly and require extensive tests for certification, with the result that they are not used much compared to commercial aircraft.
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.