Well although the design was sound for its intended purposes, great maneuverability and climb, the time of the "lone wolf" type of plane for one on one dogfights had passed. Most kills were to be had by advantage and surprise.
Some of the early Dr.1's had a bad habit of shedding its upper fabric, causing cautistophic failure. Seems the aileron was coming unhinged because of the moisture buildup inside the wing. That led to the unfortunate chain of events of the aileron coming off, taking the upper wing fabric with it, causing a failure to actually stay airborne. A couple of pilots (Gonterman and Pastor) suffered that failure and ended up dying.
Fokker's triplanes were grounded.
Subsequent planes had a beefed up aileron hinge assembly and water proof glue. Most pilots were wary of flying it.
One pilot who seemed to enjoy fighting his triplane was Jacobs. He modified his by puting a more powerful engine/prop assembly from a captured/shot down Sopwith Camel.
Once the D.VII became readily available, the triplane fleet was regulated to back up duty as it was removed from the front lines.