Except it's not Amazon blocking anything
It's not Amazon "blocking" anything -- it is a well-known issue among the Android community that certain devices ship without the core Google apps - GMail, for example -- and lack the Google Services Framework that is required to run many of the Google apps. Even CyanogenMod, one of the most-used custom ROMs for Android devices, received a C&D from Google saying "Stop bundling our apps into the ROM you distribute." (However, they do provide a separate package for the GApps.)
And Google won't allow their apps in a different app store. Again, it's not Amazon being weird, it's Google, understandably, controlling the distribution of the core apps for their operating system.
And it's actually fairly trivial to get most of the GApps running on the Fire -- all but the Android Market will install just fine without rooting the device as far as I've tried.
*Enable "Unknown Sources" (under Settings -> Device)
*Track down copies of the Google Services Framework APK as well as the APK for whatever GApps you want to install (don't try the Android Market unless you want to root the device) and place them on the Kindle Fire using the USB computer (or you can e-mail using one of the other apps, which do work pretty well, which may negate the need for a file manager. Not sure, though.)
*On the Amazon App Store, track down "Easy Installer" or a file manager.
*Using Easy Installer or the file manager, install the Google Services Framework APK first.
*Reboot the Kindle Fire.
*Install the Google Apps you want.
*A reboot may be required.
This is a LOT less painful than it could be. Trust me.