What are the disadvantages of having vortex generators?
Cost.  A set of Micro AeroDynamics VGs can run around $1500 plus installation cost.  On my plane they are installed on the top of the wing, the sides of the vertical stabilizer (fin), and the bottom of the stabilator.  I wasn't aware there were other suppliers of STC'd VGs for certificated planes. I installed mine in early 2000s, price may have gone up some since then.

They do work well, lowering stall speed while allowing the controls to be effective the same as at higher speeds. No noticeable loss of airspeed at higher power.