Your web server should be configured to not serve content just by IP and require Host header to be a domain you control. (like using server_name in nginx) Otherwise they can just point to 10.11.12.13 directly anyway.
This is an internal client using an internal IP address to communicate with an internal service... just so happens that a malicious user made the internal client talk to it maliciously.
DNS rebinding attacks being stopped by the resolver are a great place to start and something we can do. Bypassing that protection in the name of resolving using DoH just means you've made things less secure.
I don't think it should be put in the browser. It would actually made my setup less private, since I use DoH over tor.
Though configuring the http servers (like printers or whatever) and/or putting them behind a proxy on a sparate network, if they are sensitive/not configurable, should be done too.
I think you underestimate the number of things on your network that run unconfigurable web servers.