It follows that assurances to the effect that the AI industry will eventually find ways to shrink the carbon footprint of their technology are entirely untrustworthy. Any improvements that might lower the emissions caused by AI processing are bound to be treated by the industry as excess capacity, which they will promptly find ways to fill, excusing the increasing size of the footprint the same way they excuse it now: by promising that they'll find ways to shrink it in the future.
This is true in pretty much every sector of consumer tech, btw. Indie games typically lag behind the leading edge of technical specifications. Generally speaking, it's the AAA games that are requiring you to upgrade to the latest console or chip. The giant, cinematic, hyper-detailed experiences they're selling you are as much about filling excess capacity as they are about world building. I haven't seen any studies, but logically, it follows that indie games are better for the environment.