Making idempotency a protocol-level thing would be problematic with the many connection-breaking systems, even if the browser-ingress channel is TLS encrypted. You'd have the ingress proxy, maybe some IDS/IPS, maybe Cloudflare, maybe some router or gateway, some service proxy, who knows. If any of them decide to drop any headers, rewrite headers, or mis-parse them you'd lose the idempotency completely.

It does however make a difference if not the body, but the protocol-level request is supposed to be the idempotent one, but I don't know in what kind of a scenario that would apply.