I totally understand what makes IndieAuth is a good solution. And it seems really easy. For me. But I have no idea how I would go about explaining it to, let's say, my mom.
Apple is offering something very similar to what Promise does. The difference is that Apple is a commercial corporation. Which means they're in the game to make money. Promise will be in the game to make authentication easy, secure and private.
In many ways I compare the goal of Promise, with the goal of DNS. Take a commodity and make it available globally in a reliable way. Yes, it will be a single point of failure. So the job of Promise will in large be, to keep the platform secure and reliable.