"Google's not a monopoly like apple you can install any store!"
Have you tried using Android on a phone without Google Play and the kernel level Google tools? It's impossible to install most apps.
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Replying to
There's no kernel level integration for Google Play.
Play services is a set of apps which are designed to be included in the OS and integrated into it by giving them a bunch of privileged permissions, custom SELinux policy and setting them as the provider for various OS APIs.
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Many apps choose to use the Play services SDK. It's up to them if they want to provide an alternative for devices without it. If they don't, then functionality will be missing or the app may not work at all. They can still be installed and what you're describing doesn't exist.
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Despite not being designed to run without extensive privileges granted by the OS, it's possible to install Play services as a set of regular apps. It doesn't work without the privileged permissions it expects, but it's possible to coerce it into running as a sandboxed app anyway.
Replying to
There is no such thing as what you're describing. GSF ID is simply something that Play services dynamically requests from their services. It represents the Play services installation on the device. It's not part of Android itself and is simply app data so it's gone if you reset.