ELI5: Why is it that even *if* I accept cookies from a website, I still get logged out and have to log back in every time?

Isn't that the point of cookies? So once you're logged in and/or you do stuff on a website, it saves data on your computer so that you don't just end up back on a fresh page when you go back?

Then why is it that there isn't a single dang website that just keeps me logged in without issue?