I don’t think there’s anything different between what you’re suggesting and a homelab. Most people do not have a homelab and are happy to offload services like photo storage or security to remote providers.
My elderly parents have asked me about "local backups" of their cloud stuff, their Facebook history etc..
If they're thinking about the risks/tradeoffs of being in the cloud..
I think people use the cloud because there's no better/easier option today.
But at some point there might be. A home appliance (which may be similar to a homelab under the hood but the user experience is where things change) that provides a bunch of automation and home services could be quite attractive if it got to a point of being very turnkey for the average family.
Just like a TV or a gaming console is today.
My Raspberry Pi pi-hole is a Pi 2b that has been running for over 5 years and it's totally fine. It has automatic security upgrades turned on but nothing else, and it doesn't need any time or attention. It just does its job.
I have a Homelab that's a mini-PC that's quiet and does not suck lots of power and is tucked away neatly in a closet.
I think it would be completely possible to provide an appliance-like machine that would not have the problems you're outlining.
Impossible is absolutely the wrong qualifier.
A home appliance like a toaster would be in the case of an AI server are ready to go appliance that’s preloaded and confined and connect to everything in your home and help you manage it likely by just voice chat or some amount of interface.
In a way, it already exists at an equipment level - a Mac Mini or Mac Studio is very power efficient and adding capabilities to it is at an app level.
Since a solution like this would be at the level of a group of apps, that might be something to bridge.
Maybe even subsidized by the government. This will be a fundamental need.