I know there are a number of headers used to control cross-site access to websites, and the linked blog post shows archive.today's denial-of-service script sending random queries to the site's search function. Shouldn't there be a way to prevent those from running when they're requested from within a third-party site?
However, browsers will first send a preflight request for non-simple requests before sending the actual request. If the DDOS were effective because the search operation was expensive, then the blog could put search behind a non-simple request, or require a valid CSRF token before performing the search.
Mostly these headers are designed around preventing reading content. Sending content generally does not require anything.
(As a kind of random tidbit, this is why csrf tokens are a thing, you can't prevent sending so websites test to see if you were able to read the token in a previous request)
This is partially historical. The rough rule is if it was possible to make the request without javascript then it doesn't need any special headers (preflight)