I don't think adding 20 bytes to every response, which are never read in practice, will improve the energy efficiency of the internet. Not to be mean, there's just a lot of stuff in most responses that effectively nothing acts on.

Couldn't even compute this value on most infrastructure.

Perhaps I have spent too much time around curious, creative and even devious people but I suspect they would try to see which sites they could jack that number up as high as possible similar to how people share speed test results. If it became popular enough I could see Cloudflare one day doing metrics on this and making blog posts about how much power they saved.

There's a whole mini-industry around carbon accounting but (A) it's very hard to estimate accurately, (B) it will be gamed like any other metric, and (C) energy is good. We should focus on making energy cleaner and cheaper so that people can use it without guilt.