There are various level of exercises. The highest levels in the list have a much greater impact on the nervous system and should not be trained to failure. The lower 3 levels can be trained to failure. Note that training to failure is one model of training, it's not the only one.
LEVEL 8: Complex lifts (variations of the Olympic lifts, gymnastic or advanced bodyweight drills)
LEVEL 7: Big strength lifts involving whole body tension and/or spinal loading (squats, deadlifts, push presses, bent over rows)
LEVEL 6: Other big strength lifts with free weights (bench press, seated shoulder press, DB incline press, DB squats/lunges, etc.)
LEVEL 5: Multi-joint exercises with pulley apparatus
LEVEL 4: Multi-joint exercises with machines/Smith machine
LEVEL 3: Isolation work with free-weights
LEVEL 2: Isolation work with pulley apparatus
LEVEL 1: Isolation work with machines
Also understand that the study I quoted ONLY studied training to failure. They did NOT compare the differences between training to failure and not training to failure, What they established is that IF you train to failure, load doesn't matter when it comes to hypertrophy. But since they didn't compare sets where you stop just short of failure we cannot say that stopping just short of failure wont be just as effective.