The thing about "local" models for me is that they usually mean open-weight (and maybe open-source too), so they can be used locally, yes, but they can also be hosted by independent providers! With models like Qwen, DeepSeek and others, you aren't tied to a single corp, you can switch between indie providers, some of which may give you better privacy guarantees. That allows you to use the models even on devices uncapable of running them, if they have an Internet connection.
The strength with AI is with open-source models. We need to keep away from vendor lock-in and use models that allow both local usage and hosting by independent providers.