My mom just got an iPad mini, was infuriated when she discovered she can't buy Kindle books from the Kindle app like she could on Android.
The artificial restrictions Apple places on developers and users are ridiculous. And Android 5 is the first release where I can say that Android is unequivocally a nicer experience than iOS...
Agreed about Android 5 though, best yet!
Are you maybe thinking of Google blocking Amazon from including the Amazon Appstore in the Amazon shopping app? That's a different issue and, more importantly, that doesn't really affect what's possible on Android, just how convenient it is. After all, anyone who wants to can download the store Google blocked from Amazon directly.
I think you can argue that a browser itself is an app store (you download and execute (web-)apps with it). But Apple does not allow the installation of different browser engines, so you can still not install an app store on your device.
But not to my mother.
I would guess (and only guess, I haven't tried to look for any numbers) that the percentage of people who go out and install an alternative app store, let alone Amazon's, is quite small (especially once you take out the HN audience)
She has an Android phone, with which she can buy books through the Kindle app (without messing with a website).
She has an iPad, on which she can't buy books through the Kindle app, and she does have to go through a browser to their website.
To her, the Android experience is better because of this (she reads a lot).