Removing "broken links", or requests that result in 404/410 errors, avoids wasteful requests.
Page Speed recommends:
Avoid using redirects to handle broken links
Wherever possible, you should update the links to resources that have moved, or delete those links if the resources have been removed. Avoid using HTTP redirects to send users to the requested resources, or to serve a substitute "suggestion" page. As described above, redirects also slow down your site, and are better to avoid as much as possible.
Feel free to contact us with your suggestions, links or ideas!