You should do some research. This happens all the time. Companies do this as an alternative to dividends. Where do you think dividends come from? (Earnings.)
Share buybacks are absolutely not the same thing as a company taking themselves private. When a company repurchases shares, that stock is then "treasury stock" which has no voting rights, cannot receive dividends, and must be under a certain legally set value.
Yeah I know that. Obviously, it wouldn't own itself. That doesn't make any sense. A small pool of insider investors, the management, would ultimately own it.
But they'd have to pay for it with their own money. They can't use Apple's cash to pay for Apple. When Apple buys its own shares back, it effectively increases the ownership percentage of its remaining investors -- who still own all of Apple. Spending all of Apple's cash on buybacks wouldn't fundamentally make it any cheaper for anyone to take Apple private.
A company cannot own itself.