Sure, but the Google Play store has a privileged position on users' phones that can perform actions that a 3rd party app store cannot, namely installing and updating applications.
And Google Play only really has that privileged position because they develop Android. I think it's honestly pretty clear cut here.
Unless you buy Samsung phones, which means 25-30% of all Android phones, which come with the Galaxy App store in the same "privileged" position. Or any phone in China, where the Play Store is not available.
Also I don't remember having trouble with the Amazon store keeping apps up to date for me.
And Google Play only really has that privileged position because they develop Android. I think it's honestly pretty clear cut here.