They don't work well in my experience.

What I want is to get my home screen back exactly as I left it: I've not found anything able to pull it off on Android though.

Ideally it would be an exact flash image of the phone.

Adb backup exists, though I haven't tried it, and Google cloud backup does this. However, if you trust Google, you probably already trust the US.

Unfortunately, I don't know of any other app that does this on an unrooted phone.