They use a third party domain just because that way they can track the user actions with cookies, for example Google can track your navigation across multiple w

They use a third party domain just because that way they can track the user actions with cookies, for example Google can track your navigation across multiple websites, and thus propose to you more relevant ads. Also using a different domain was simpler and cheaper, since you don't have to host the AD content and metadata, just include the JS from the AD provider somewhere in your HTML. Now that thanks to EU laws and browser imposing restrictions about third-party cookies it's more difficult, the whole "serve ads from other domain" may not be that relevant anyway. If you use a random wildcard subdomain... just serve them from the main website, what is the difference? On the other side with a proxy just route the AD requests to another server if it needs to be, of course you have to find a way to distinguish which requests are for AD and which are not, something you can do with some sort of signature in the filename, so that only the server can know which requests shall be handled locally and which one forwarded to the AD provider server.