This isn't an issue of Android being more "open". Google baked-in one-sign in features into Android, sure, just as Apple did with iCloud. But you can't do this for other 3rd party apps on Android. You can't sign in on one app, and continue being signed in on another app (at least not in the way that you complain Apple should allow).
I do like your idea, and agree Apple should allow this. They should also allow changing the default applications, and allow better access to internet APIs, so Mozilla can actually make Firefox for iOS. But that aside, what you're complaining about isn't something Google does either