I have the Amazon Appstore on my Android phone. Google does not allow Amazon to compete on feature parity with the Play Store. Amazon's Appstore cannot do background installation of apps, batch installation of apps, or automatic upgrades if the device isn't an Amazon device.
If I click to install an app, I want it to install in the background instead of booting me out of the foreground app to show me the installation screen. As a result, any time I want to upgrade or install an app using the Amazon Appstore or F-Droid, I have to click through a dozen install screens that I can't get through all at once or have them install in the background.
Google has restricted Android such that only the Play Store can implement background installation of apps, batch installations and automatic upgrading of installed apps. F-Droid can implement those if you give it root access, but manufacturers go out of their way to prevent users from rooting their devices.