note that you probably need to trust the remote household with your data
Probably not actually. Borgbackup (and any sensible encrypted backup system really), does client side encryption. So the data should be encrypted before it's even sent down the wire. The remote household shouldn't be able to access the data without the encryption key/password.
I mean, they will have to trust the remote household not to destroy the data, but that's pretty much an unavoidable limitation.
Honestly, it already looks ridiculous.
To be clear, I think the automation of jobs is, at least in the immediate, a serious problem, with real consequences. The problem is real. The issue is that objecting to the technology itself is idiotic. That's not a fight you'll win. The technology exists. People are going to use it. And in the long run we'll all be better off for it.
There's serious conversations to be had about how we use AI, and how we deal with the consequences of its use, and especially how we manage the transition. But you can't have those conversations with someone who insists that AI is the devil and that we need to stop it, and who gets mad at you when you suggest otherwise.