You are right that a lot of guys use partials at various times. I think this is usually to learn how to exploit equipment (another topic). Do you wear a bench shirt? Do board presses improve your raw bench? I'm sure they don't change the position of your sticking point.
You are also right that an experienced lifter can vary their squat depth easily.
What I have found is that a beginner who ONLY learns high squats has a hard time going deeper. It has to be entirely relearned. I find that they aren't in the right position to just go a bit deeper, they haven't broken at the hips, and when they try to go deeper, the knees come forward a bit more and then they are stuck. If you go part way down in the form that is usual for full squatting then it is easy to simply go a bit further.