Great Comments, Thanks
I love all of the comments, thanks.
First, you cannot simply sideload a Google app... have to first install the Google Services Framework apk first. I have instructions for this here: https://plus.google.com/u/0/113139726938588189465/posts/3UZGtF8H9aU
The problem is, your typically Kindle Fire user is probably not tech savy and probably won't want to take these extra steps to sideload apps.
I also have a post on 'must have' Kindle Fire apps here: https://plus.google.com/u/0/113139726938588189465/posts/ZaKkJKMbLba
Ultimately I think this is an Amazon AND a Google problem and it's all about control and licensing for the app market... be it Amazon's or Google.
Shame on Google for putting hooks in stand-alone apps like Gmail that require Google Services Framework (you don't need the Google Services Framework for the iPad). Shame on Amazon for not making popular Google apps a part of the Kindle Fire user experience.
One other note - the Kindle Fire OS is a "wrapped" version Android and not a "fork" as Linux users understand forks.