And it doesn't even need a page refresh; it could use a 204 No Content response. Potentially an yet-cleverer static browser system could also use 206 Partial Content to replace a portion of the page.
But at that point, it's no longer "purely a document," it's still an app, just one that runs entirely on the server instead of partly or mostly in the browser.
For the web to be just documents, you have to go all the way and remove state entirely. Idempotence all the way down.