I don't think you're following what I'm saying. You can be more stable or less stable while turning. A lower PMOI car is inherently less stable, meaning a jerk of the wheel will have a more dramatic effect. What might be good for an F1 driver, may not be for Joe Average. Some stability is good, and the more centered you make the weight, the less stability you have, hence "inherent destabilizing effect".
Again, weight distribution and PMOI are 2 separate concepts. Just because you have 50/50 weight distribution does not mean that you have a low PMOI, and a low PMOI does not mean that you have 50/50 weight distribution!