We may be running out of disagreements, but I still think you're too sympathetic to a fictional seamlessness of character and personality as a justification for nosiness. As you say, the desire to sniff the soft and fetid underbelly of the great and famous is what drives readers in droves to revelatory biographies. But it isn't because we believe there is a connection between total character and achievement. Achievement requires character, but it is character of a very specific kind--the kind that keeps you at your desk to write War and Peace or at the staunch helm of the state through the Battle of Britain. Such achievements can coexist with every kind of purely personal weakness and lack of nobility.
I think the widespread interest in holding up great achievers to personal derision is partly due to envy: Too many people hate the success and sheer unavoidable size of those who have managed to summon up from their miserable humanity something superior to what they were as a whole. The resentment turns into glee when prominent persons are all too easily revealed in their pitiful human smallness.
There is also a more innocent pleasure in just knowing as much as possible about the lives of people to whom you have become attached at a distance, through their works. Not only the politicians, but the writers, composers, performers, and scientists whose creations have had a big impact on us inevitably get charged with emotional magnetism. We can't help wanting to possess them, particularly since they don't know and don't care about us, except as members of the anonymous audience. The one-way intimacy that we are offered by biographers or journalists, without the consent or against the will of their subjects, is a way of appropriating for ourselves a larger share of these public figures than they themselves had it in mind to offer when they made their bid for fame and achievement.
So there is a built-in source of danger to the privacy of the prominent, as there is to every valuable prohibition. We build such barriers because we know the strength of the temptation to transgress them; and once they have been destroyed, it is very hard to rebuild them.
We could probably go on for weeks about the analysis of political liberalism, but let me say just that there are many forms of disapproval that fall between condemning murder and hating butterscotch. Preventing harm to others is not the only ground offered in our politics for restrictions of liberty. We accept collective decisions for some kinds of paternalism--seat belts, motorcycle helmets--and for many public goods. But there are important demands for collective control where harm to others may be alleged as the reason, but where it is really a cover for direct moral disapproval of an activity that actually has no unwilling victims. Prominent examples are drugs, homosexuality, pornography, and assisted suicide. Luckily our society has left behind the enforcement of religious orthodoxy, but the world has not. The idea that the president's sex life is everybody's business evinces the same mentality that would gladly control the limits of permissible sex, and various other private choices in the conduct of life, by majority vote. Democracy, rightly understood, does not give us that kind of collective authority over one another. But I suppose you would agree.