I came across a couple things today which I figured I should post here for the sake of completeness.
First, Caddy actually does pass along the original Host header by default like I had thought before, though it of course also sets X-Forwarded-*. Nginx, on the other hand rewrites the header by default.
Second, there is actually a case where you do need to rewrite the Host header: if you are using HTTPS to encrypt traffic between the reverse proxy and your webserver, you need to set the Host to match the cert! In this case you would be forced to rely on X-Forwarded-Host to know the real host.
