Er... are you sure android apps for gmail, calendar, drive, youtube, maps etc. and not to mention, the play store for android exist for the sole purpose of blocking third parties? Surely they have their own utility to users... no?
Does Google forbid 3rd party app stores on a device with full Google Services installed?
Android licencing means that no company is allowed to ship both Google Android and non-Google Android. This means that to ship Google Android on the phone they (Amazon) would have to ship Google Android on all Fire tablets too.
In addition under the licence Google apps need to be both installed (you have to have all of them, you can't pick and choose) and placed in particular prominent locations (so the Play Store needs to be on the first home screen). This would almost certainly mean that Google's store(s) would be have as good if not better positions than Amazon's own stores on the device. More than that there are restrictions around app stores which compete with Google play which would, at the very least, restrict Amazon's ability to pre-install and operate their own app store.
Given that Amazon's reason for making these devices in the first place is to sell content - videos, music, books and apps - stock Android is to all intents and purposes a non-starter for them.
See here: https://www.theinformation.com/Google-s-Confidential-Android... for more information.
Amazon's goal should be for it's apps and services to be fully competitive with everyone else's regardless of what phone they are on - iPhone, Nexus, Galaxy, Fire, shouldn't matter. I really don't see what the problem is with having Amazon's apps and services installed on the phone by default right alongside the ones from Google. Let the user decide. If users tend to prefer the Google stuff to Amazon's then they're not going to buy an Amazon locked-in Fire phone anyway.
Amazon's problem is that their apps don't come pre-installed on anyone else's phone by default. Making their own Fire phone solves that problem. It doesn't solve the problem of making Amazon's apps actualy competitive with everyone else's. That problem can only be solved by actualy making their apps good and desirable. If they aren't, locking Fire phone users into them isn't going to help sell any Fire phones and therefore isn't going to help gain exposure for Amazon's apps anyway.
Nexus is a reference design. So, I'll just copy Nexus but bundle Amazon Prime with it. What's not to love? So AMZN has to bundle their Amazon App or whatever on the phone; that's a given.
Unless, of course, GOOG has decided to actually make money off the Nexus phones, as indicated by their Nexus 6 pricing. But that's just opening up a market for a less expensive clone to be the logical replacement for the Nexus 4/5.