I think it's possible to create a hybrid whereby your personal AI - has access to those external systems to check public (maps, search) and cloud data (calendar, mail).
But it stores the private data about your location, your searches, your purchases. this could even be an encrypted private fire-walled bit of cloud rather than a robot in your house.
The point being your AI is serving you. And you can delete/edit this private data (or even the whole AI) if you wish.
This is spot on. I'm okay with having my home automation system tap a weather API to collect data. But I don't need an Internet service to know the thermostat settings in my house.
I've designed my home automation system on the concept that the only route to the Internet is my computer (and therefore, my home automation software). My computer is a secure, well-managed intermediary that can store my data, and decide when and how to receive and send data to the Internet.
The idea of dozens of Internet-connected devices in the home is :terrifying: in comparison, especially considering that badly-secured IoT devices are now powering some of the biggest botnets out there.
My light switch, however, cannot talk to the Internet. It has local-only communication protocols that are simple. It knows how to be told to turn the lights on or off or dim or a handful of other settings, but it's literally incapable of doing anything else... and why would I want anything different? Why should my light switch have Bluetooth and Wi-Fi and software updates and a miniature flavor of Linux... It's a switch!
Your description sounds like a very intelligent cache/proxy.
When my AI can talk directly to your AI, we can transfer mail etc without cloud services. If it knows our social network, perhaps it can remotely store encrypted backups of our data, but only with people who we already trust.
But it stores the private data about your location, your searches, your purchases. this could even be an encrypted private fire-walled bit of cloud rather than a robot in your house.
The point being your AI is serving you. And you can delete/edit this private data (or even the whole AI) if you wish.