Without the rest of Google, Youtube doesn't exist, because it doesn't make any money and it costs a shitload of money to run.
Google's actual businesses aren't Android, or Chrome, or Youtube (not including Youtube TV). They're AdSense, Google Cloud, their hardware division, the Play Store, the aforementioned Youtube TV, etc. Those are the things that make Google money, and really the only things you could realistically split off from Google and expect to still exist in a year or two.