Upstreams were very limited, and HTTP requests send cookie data in each GET.
For instance, if you had a 128kbps DSL upstream and each request was 2KB (loaded up with cookies), you're already limited to 8 requests/second. A cookie-less domain for small resources helped this a lot.
A separate domain name for static assets would not receive any cookies of the actual site. This means less data transferred and in theory a proxy closer to the user could more easily cache these requests, even for multiple clients.
You are making the assumption that the domain pointed to different physical servers. To get the benefits of what everyone else is describing it does not matter what the domains actually are pointing to.