Part of it is removing extra data when requesting style sheets and such - there's no need for a browser to send all of the set cookies it has for your web application when it's fetching styles, so people buy separate domains for them.
The problem is you can't explicitly tell a browser to fetch a cookie from cookie.example.com - and when you have multiple subdomains which rely on the cookie, plus analytics software which sets it for the whole domain, you can't do that.
Sort of: If you only ever need a cookie set on app.example.com, you can do that and use assets.example.com. It'll work for simple applications and not much else.
Things like Google Analytics also set cookies by default on *.example.com so you'll have to figure out a way around that.
