Earlier quoted context omitted.
It's a defense in depth mechanism: when you allow user-generated content uploaded on your main domain, somebody will find a way to break your security system and make that content executable on the user's browser. When doing so, an attacker can steal cookies, and/or invoke APIs for the user. Now, there are of course ways to avoid that, but in the end, if every other system fails, being on a domain without any API and…
Is this also another case for hosting your main site on www.example.com instead of example.com? This way you could have cookies only on www.example.com while hosting user generated content on assets.example.com or whatever sub-domain you want that's not www?
Having a total different domain help highlighting that it is not official content.