From what I understand that CDNs are meant to physically cache your static files in multiple regions closer to your users. However, I've noticed a few websites that when a page is requested from their server, they grab the asset files from their cdn, process them (compress, minify, etc.) cache the results on their server and then send them to the user requesting the page.

This doesn't make too much sense to me. Wouldn't processing the files on your server eliminate the gains from using a cdn? Is this a normal way of doing things, or am I not understanding the whole asset management concept?