If that's what you're after, tou MITM it and setup a proxy so Claude Code or whatever sends to your program, and then that program forwards it to Anthropics's server (or whomever). That way, you get everything.
I'm aware that this is possible, and thank you for the suggestion, but surely you can see that it's a relatively large lift; may not work in controlled enterprise environments; and compared to just right click -> view source it's basically inaccessible to anyone who might have wanted to dabble.