Digression aside, the acknowledgement of the states is a neutralization of pure people power. It is the same reason that the Supreme Court is not elected, and executive appointees are not elected. These are things that are intended to be a check against the people. This is also why the tax-exempt status of churches is supposed to depend on the fact that they are to be politically neutral, and why Kennedy's Catholicism was such a hot issue when he ran for office. This is why charities frequently remain neutral in political discourse, why HN was divided on whether a business should be allowed to take sides on a political issue. This is why you're not allowed to discuss who you're voting for, or campaign for a candidate or issue, within a certain radius of a polling station.
Because "one person, one vote" never is. In any group of people larger than approximately 25 and definitely larger than 150, you will never actually get "one person, one vote". You will get political parties, who give you flyers saying "Vote for these 5 dudes, vote yes on A, B, and D, vote no on C and E," and those flyers will be followed to the letter.
It is probably possible to maintain the argument for "one person, one vote" despite all of these reasons not to, of course. I'd like to see the argument made that can account for the problem of demagoguery, the problem of charisma, especially enhanced as it's been by the advent of television. I haven't seen it yet.