Apple is a commercial corporation, and one of the biggest (by market cap) companies in the world. That gives me confidence that they'll be around for a long time, have sufficient resources to invest in security and reliability, and they have a well-established reputation for a focus on security. They do other things I don't like[1], but I think this is one area where they're setting really good precedent.
In addition, it's going to be difficult getting any sites (outside of maybe the crypto/grey-market) to adopt an auth system that doesn't let them contact their users. This is also I think a big failing of IndieAuth.
If a site needs to contact the user, it's reasonable to ask for eg. an email. But now the intent of asking for an email has to be crystal clear, which makes you and them more aware of what data you are actually giving them.
Apple sure is doing some good stuff with their authentication solution and their efforts to help people with healthier passwords habits. I'm still not too fond of having such fundamental infrastructure owned by a private company. Would you be comfortable handing over DNS to Apple?
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.