The company can't "buy itself" into a private company either. It doesn't work for a whole host of reasons, one of which being that they aren't sitting on the ~600 billion in cash that would require, another being that buying a bunch of stock back is fundamentally not the same thing as being a private company. But also, if you buy all the stock back, it means by definition that you have liquidated all value in the company (or else we're assuming that the market undervalued the company so much that it thought nothing but the cash on hand was valuable).

If you assume that Apple is going to borrow the 600 billion to buy all its stock, then you are effectively saying that whoever's left holding the "private" company is holding a 600 billion dollar loan. I do not share your optimism that anyone can get a loan large enough to buy Apple.