The problem associated with riding the reset only to that minimal point is trigger freeze. If the trigger is only allowed to move forward enough to reset and there is thus no margin for error, as soon as the shooter gets tense (from stress, from pressure, from trying to move as quickly as they can, maybe because of external pressure, etc.) the reset gets short-stroked. Since there's no margin, trigger freeze happens.
I've seen releasing the trigger ONLY to the point of reset to be pretty commonly taught in defensive training. That's how I was taught in the beginning. At one point, even though I still believed in the idea as 'better', I caught myself letting the trigger further forward than that (but still maintaining finger-trigger contact) when trying to shoot accurately at greater speeds. In trying to do that, I unconsciously discarded the actual technique of riding the reset, even though I didn't intend to. It was an unconscious solution to trigger freeze.
Later, I heard about the other side of the coin, where people talk about slapping the trigger (finger going all the way forward inside the trigger guard and back to hit the trigger again.) This is usually discussed in the context of competitive shooting, using a gun that has a very short and light trigger. I think this extreme may be impractical with guns that have more difficult triggers.
At this point, I make sure students in a basic pistol class understand that there is a reset point and they do have to let the trigger at least that far forward in order to fire again, and that they should maintain finger-trigger contact until they stop shooting, but that it's ok if they let the trigger further forward than the reset point. After that, and as people keep training and developing, I think they will unconsciously use trigger technique appropriate to the shot at hand. I probably do sometimes still ride the reset - when I'm shooting a difficult enough shot that trigger freeze simply isn't going to happen because of how much the gun must be settled out of motion and how careful I have to be with the trigger. On easier shots, I tend to let the trigger out further.