My reasoning was this:
Part of Le Chatelier theory is that the system will attempt to counteract the change, but will never fully counteract it.
Thus, I found it more likely that it will undershoot it, and thus approach it asymptotically, rather than overshoot it and come down to it.
I disagree. Humans have known for a long time that a fundamental difference exists between nitric acid and say citric acid. That is reflective of a primitive understanding of strong and weak acids that was later clarified by Arrhenius.