Maybe someday that will be a realistic endeavor, but it would take a lot of effort to set up and maintain your own personal versions of all of google's services, and integrate them
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.
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.
https://en.wikipedia.org/wiki/Intelligent_agent
Perhaps using Urbit as the network architecture since it already has pki. As Yarvin calls it, true 'personal cloud computation'.
Really it's the only sane way to live in the 21st century.
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!
It's just not easy to do, both in setup and maintenance effort. Most people would not care about their privacy nearly enough to justify that.