For one, you’re wrong about TLS meaning only your infra and the client matter. Some big corps install a root CA on everyone’s laptop and MITM all HTTP/S traffic. The one I saw was Bluecoat, no idea if it follows your expected out-of-spec behavior or not.
For two, this is likely to become incredibly limiting at some point and require a bunch of work to re-validate or re-implement. If you move to AWS, do ELBs support this? If security wants you to use Envoy for a service mesh, is it going to support this? I don’t pick all the tools we use, so there’s a good chance corporate mandates something incompatible with this.
You would need very good answers to why this is the only solution and is a mandatory feature. Why can’t we cache server side, or implement our own caching in the front end for POST requests? I can’t think of any situations where I would rather maintain what is practically a very similar fork of HTTP than implement my own caching.