Strange comparison. We should remember that the difference between a government and a company is who owns them. Governments are owned by the people, and many times throughout history, it became obvious to the population that they could not trust a private company to manage their fancy new communication network. And so, they had their government do it, so that they would have a say. That’s what democracy is all about.
They aren’t new problems. Facebook provides communication, not friendship. The friend component is just a network address book of sorts, effectively no different from a phone number. If the phone company were allowed to replace phone numbers with references to a centralized lookup table, they would certainly do it. But it’s illegal, thanks to over a century full of public outcry and contentions just like these.
Of course there are several attempts at building a decentralised 'social' network like this, e.g. Diaspora and GNU Social. Thus far they have not taken off other than in limited circles.
I don't mean to claim that Facebook's done nothing wrong. But ultimately, there are uncomfortable tradeoffs involved in friendship-as-a-service. Expecting an completely non-creepy version of Facebook is like expecting a completely non-controversial version of government.