You do know that fingerprinting is a thing, right? Private browsing is designed to keep your local device clean of your tracks, not the wider web. At all.

Telling Facebook "hello, I am visiting baddragon.com from Mozilla Firefox 63.1 on Obscure Linux in Podunk, Saskatchewan, population 32" is barely an improvement over telling them "hello I am John Q. Smith and I am visiting baddragon.com".

And of course, private browsing is generally per-instance. Log in to your Google account in a private tab? All your other "private tabs" are also logged in to Google until you close the private browser.