Earlier quoted context omitted.
It's a shopping website. It's sorta hard to do cart management without cookies.
Just put a session id in the URLs.
Session cookies on the other hand can be marked as http-only, mitigating XSS in many browsers (there are some that still screw this up with XmlHttpRequest) and by not having the session id in the url, the id is much less likely to be shared with others, nor to appear in search engines.
Also, it keeps the URLs nice looking.
So why exactly would one want to disable session cookies?
Because of all of the above reasons, I'd much rather keep users with cookies disabled away from my application than to subject them to the ugly URL fallback which will impact their security much, much more than the perceived privacy loss of session cookies (which go away when you close the browser)