Non-technicals don't know how LLMs work, and, more importantly, don't care about their privacy.
For a technology to be widely used, by definition, you need to make it appealing to the masses, and there is almost zero demand for private LLM right now.
That's why I don't think that local llms will win. There are narrow use cases where regulations can force local llm usage (like for medical stuff), but overall I think that services will win (as they always do)