You can turn a local model on and off as needed, and it will still function as expected. If you turn off your self-hosted server, you don't get email.

With self-hosted email, you need persistent infrastructure and domain knowledge to leverage it. With a local model, you just click a button and tell it what to do.

With email, there is a necessary burden to outsource. Your local model is just there like Chrome/Edge/Safari is just there, there is no burden.

But AI is not about connectivity. Local models are just about as useful without an internet connection. Also, the hardware can fit in a small enclosure.