When we're talking primal movement patterns like deadlifts, squats, presses, and more, we should take advantage of the fact that we can load them up significantly more than many other movements. They'll serve as the foundation of our strength. And due to the compound, multi-joint nature of each movement, you'll get great benefits from going heavy – 6 reps or under per set.
But that doesn't mean you have to hit heavy triples every time you enter the squat rack. You should, however, use sets of 6 or fewer reps for these movements simply because of the fact that the larger the movement, the more room for technical error.
Even if you're squatting far below your max, the implement you're using will likely be that much heavier than that used with many other training methods. Relying on your coordination becomes a bigger deal, and you're simultaneously at greater risk while setting yourself up for bigger gains by selecting such exercises in the first place.
Focus on quality over weight lifted, especially as you tack on years of training experience. This will become invaluable to your health, true strength, and recovery. Control your eccentrics (negatives) and learn to kill momentum, using perfect form on every rep.
When it's time to lift lighter, it doesn't mean you need to do sets of 15-20 to compensate. Keep the rep range in the same area, and just add volume to your workout. Do more sets and cut your rest time to get the same conditioning benefits while maintaining quality. Where these big lifts are concerned, 4 sets of 5 with short breaks can be just as effective as 1 set of 20.