> The Android OS is intentionally crippled to work only with Google Play push notifications, and there are no 'stock' ways to use an alternative without modifying the OS.
And distribute the modified OS to all your customers how exactly? You could probably sell your own android based phone as long as you find a single manufacturer that isn't part of Googles OpenHandset alliance or bound by the Play Store license to only sell Google approved Android. Alternatively you could limit yourself to India and China where Google cannot enforce these terms. There really isn't any point in pretending that Android is an open OS in the west. It is Googles proprietary stack or nothing.
If it were that easy as an overall solution, non-OEM Android forks would be mainstream. They're not. I hardly know any people using non-OEM Android.