You have that backwards. The only thing you gain from running local models is privacy. It is not cheaper, it is not more efficient. You are actively hurting the environment MORE by using a local model on your own. LLM efficiency sky rockets the more users there are on a single loaded model.
IMO the only way we get to efficient LLM usage would be by having very efficient non frontier models running only for its local community to use, where you can have assurances on whether its power source is clean or not. That doesn't help with the plagiarism aspect though