The play store is unavailable within China anyway, so alternatives certainly exist.

The play store is not the sole way to distribute apps. You can download the .apk files, or get them by mail, or use another play store that has the same apps. The play store is just a repository of some apps.

I believe the Play store is treated 'special' though - F-Droid can't install apps in the same way unless you're rooted and install the priv-app.

On a phone licensing the Play Store sure. But on a Huawei phone free of those restrictions they can make it use any store they want without any special restrictions. Of course, it becomes a question what that means for security, but still.

I did not root my phone yet, and I install apps with f-droid just fine. The only thing I had to do, if I recall correctly, was enabling third party apps instalation

Try it again and watch the process closely. You'll get an additional prompt when you use F-Droid that doesn't appear with the Play store.

Indeed there is an extra confirmation step, and it freezes some processes (specifically, those that alter the screen, like red shifters)

That seems like a violation of anit-trustlaws. I'm surprised the FSF hasn't pursued this route against google.

I don't think that the lack of Google Play would be a huge problem. I use Android devices in the US and don't use Google Play.