Language models at the moment do require a significant amount of power especially during training, but consider this. If you were to run a language model locally on your phone or laptop (which is likely to be the case in the future) it may not require using the internet at all. It may even use less power compared to have your query sent to a search engine server. But to answer your question, at the moment I would only suggest using a language model for language heavy tasks like writing emails and querying information that does not require recalling specific facts.
spam fails_task lang_mismatch pii not_appropriate hate_speech sexual_content quality toxicity humor helpfulness creativity violence