Session variables. If people would use those and not just cookies. It'd be better.
And how exactly do you think session variables work? How do you link a browser to the session? Cookies!!!
Yes, I know you can put a god damn session id in the URL query string, but that's annoying, unreliable, and insecure. IF someone navigates your website for a bit, puts some stuff in the shopping cart, then just goes back to your homepage by stripping everything but the domain name off the URL...TADA!!! You've lost their session!!! Or if they jump to a different part of your website via a bookmark from a previous session...TADA!!!! You've lost their session. Or if they copy their URL and pass it to someone else/post it on a forum...TADA!!!! Someone else is now using their session (yes, you can "solve" that issue by linking the session by a secondary authentication variable like IP, but then you run the risk of having your website broken for anyone that moves between IP addresses).
In short, I've never seen a good, clean, reliable way to link a user to a session that doesn't involve cookies. If you've got the magic solution to that, please...I'm all ears.
Now if you mean websites should only use session cookies instead of persistent cookies, and the "deny all cookies" option only denied persistent cookies (does it do that already? I have no idea), then yes...that is a workable solution for most cases. Off the top of my head, I think the only thing you lose there is the ability to persist your login between browser sessions. But then again, if someone doesn't mind session cookie but dislikes persistent cookies, they could already set their browser to clear all cookies on exit or use a private browsing mode, and then all current websites would work perfectly fine.