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.
Aviation is one of the easiest cases because the amount of fuel burned is tracked and ~100% of the carbon in the fuel becomes CO2. Since there's currently no good alternative to hydrocarbon fuel, it's also a good case for biofuel or carbon capture (not offsets which are mostly fake).
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.
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.
IMHO it’s better to bake this information into the price of the resource and then include the externalities for polluting by using a Pigou tax, or as in the EU, with a cap and trade system (EU ETS).
And that’s probably one of the reasons that you need to pay for using the best version of ChatGPT and similar products.
