While private browsing is not actually private I feel going so far as to say it does not stop websites from collecting info on you is maybe a bit too far.
The site can still collect information about you, yes. But unless you sign in while in private browsing or the site is using some sort of user-agent / IP trickery it won't be automatically tied to your accounts. None of the cookies or local storage are shared across private/non private browsing.
Personally, I use it mostly to see what websites look like when I'm not logged in or if I want to access something that can only be accessed while logged out without actually logging out which is surprisingly common.