When permanently removing a page from your website, are there any practical benefits to setting up a \"410 GONE\" HTTP response for the URL (vs. letting it 404)?
Yes, the 410 Gone
HTTP status code conveys that the resource requested was once available in the past, but it has now been retired or made obsolete.
The 404 Not Found
HTTP status code could imply that the website has been incorrectly updated so as to be missing a file that would normally be defined there. It could also mean that the requesting client referenced a resource that never did exist and probably never will.
The 410 Gone
status can have more immediate SEO implications because it tells search engines that the missing resource was intentionally removed. That should hasten the reduction of future search references to that page more so than the 404 Not Found
status.