That's a good point. I rescind my argument that training is necessarily more expensive than sum-of-all-deployment.
I still think people overestimate the power draw of AI though, because they're not dividing it by the overall usage of AI. If people started playing high-end video games at the same rate AI is being used, the power usage might be comparable, but it wouldn't mean that an individual playing a video game is suddenly worse for the environment than it was before. However, it doesn't really matter, since ultimately the environmental impact depends only on the total amount of power (and coolant) used, and where that power comes from (could be coal, could be nuclear, could be hydro).