AIUI, the git ssh protocol is just the git protocol tunnelled through ssh. So why do they need different mechanisms for signalling V2?
Deploying Git over SSH entails locking the precise command line executable by the public key you use to authenticate. Locking SSH SendEnv down is mandatory too, otherwise thousands of people would have shell access to GitHub.com! This isn't even theoretical, there was an environment-related bug not 5 years ago involving Git. At least BitBucket was impacted, I think GitHub were patched before it was announced
As you point out selectively allowing a new environment variable could open a can of worms for shared hosts like github if they mess up their implementation.