One issue is that the make the aircraft more unstable. Consider what happens when you let loose an arrow with the feathers in the front, not the back.
This is counteracted in modern fighters through computer controlled fly by wire that make massive numbers of control inputs/corrections every second.
Still seems like there was some other drawback to maneuvering in combat that canards limited things. Maybe not.
They have been around a long time. While not a fighter, the B-70 bomber had them in the early 60's.