Lemmy will rewrite the image URLs when saving a post.

But instead the URL should be rewritten when loading the post. That way the original URL wouldn't get lost and it would also work for old posts.

You're missing a lot.

I've done exactly what I described in my comment for the last 8 months: it's been a UI feature of Tesseract since last October.

It proxies any image or direct video from any source you haven't blacklisted. If you have the proxy option enabled in your settings, all image URLs are re-written to go through the proxy. If not, then it uses the regular URL directly. It also caches with an admin-defined policy.