(Yes, there will still be issues if you use apps that require Google's remote attestation, but at least in Europe, many banks etc. do not require it.)
Play Integrity is a remote attestation scheme by which apps can ask the OS to prove to a remote server that it is unmodified. It allows apps to refuse to run on devices with root or third-party ROMs.
Play Services is a set of libraries and APIs for things like network-based location, push notifications, and advertising. Nearly all Android phones include it, and users of third-party ROMs can add it at install time (but not later) with packages like MindTheGapps. There's an open source substitute called MicroG that allows most apps to run without it.
You're right in your elaboration, but I didn't mention which one it is. My primary concern is that it forces me to log in to my play services account, which I haven't agreed to so far.
> There's an open source substitute called MicroG that allows most apps to run without it.
It's not for the lack of trying and I probably wouldn't even be complaining if it had worked. Phones are getting harder to root these days, much less install a custom ROM. Everyday feels like the ecosystem is tightening around us.
The same in India. I can't use even the government weather app and the disaster alerts app without signing in to google play.
Seeing that this malpractice (of forcing the users into Google's surveillance net) is widespread among seemingly unrelated agencies like banks and government agencies of several nations, I would really like to know who is peddling this draconian scheme among them.
I want to send some angry rants to the app owners/developers and ask for those malicious peddlers to be permanently banned from further interference in cyber security matters of these institutions.