Amazon doesn't require you to use their payment system with your customers to host your app on AWS. Paypal doesn't require you to host your apps with them to use their payment system. Mozilla doesn't try to stop you from using Firefox, or the Firefox-based Tor browser, to visit arbitrary "dark web" sites, and Debian doesn't try to stop you from adding arbitrary third party repositories to apt. Let's Encrypt doesn't even require you to use their own software to verify your site. This concept of "you can't just sell someone a screw driver because what if they kill someone and you were liable" has no basis.
Google could refuse your business for an individual component if you tried to use that component from them, but then you could just get that component from someone else. It would still be an advantage to be able to use one service for hosting and another for payments, even if zero of those services are Google.
And the problem with Google Play is the weak competition. If it was easier to use something else then they would lose more business from making poor refusal decisions (harming their reputation), by charging a high percentage, etc. Then they would either have to improve or lose their status as the dominant player. Reduced barriers, more competition.
The proposal was to host your own app store which doesn't rely on their infrastructure.
And if you are using Google's identity system—in what way are you not just back to publishing on the Play Store? Through the identity system (and associated developer-reputation system) they can control who can or cannot publish on your app store. So it's really just their app store. It's your UX, but it's their guiding hand, just as if Google were on your board of directors.
Really, there's no point in them letting you have your own app store which relies on parts of their infrastructure, since they can tell that any implementation their legal dept would okay is a lose-lose that no dev would ever be interested in taking part in. To detach any liability for the results from them, you have to do it all the app-store stuff yourself. Which is exactly what mobile OEMs do.