If you implement Sign In With Apple, you don't have a relationship with your customers anymore. They're Apple's customers, and Apple can take them away at any time.
Specifically, if you implement Sign In with Apple, then they are still your customers as much as ever, they just might choose to hide their information from you because they don't trust you, which means that the power in the relationship is transferred to the user instead of the app developer.
I think GP is absolutely right here. Apple can take the customers at any time for any reason. Apple could ban you from using Sign in with Apple simply because Tim Cook doesn't like what food you eat for breakfast. So, I have to agree with GP that these are Apple's customers at this point.
I actually think this wouldn’t really happen in practice as consumers are quick to respond negatively to this behavior, so I’d be shocked if Apple actually did this without some darn good reason (I imagine it will also include removing said app)
That hasn't stopped Apple from remove apps or preventing updates -- clearly inconveniences on users -- for whatever reasons they want. It has happened and it will happen again.
There is no check on this unless your app's audience is Netflix/Spotify/Facebook huge. If you're just an average developer you can be killed off at any time.
Hardware requirements for software is a decades old concept, and it’s true they deprecate and obsolete supported software and hardware on for older platforms, but it’s rare I’ve seen Apple taken a user hostile approach here within supported lifetimes though it has happened yes it is rare.
Their developer experience on the other hand does not see the same care and attention a lot (most even) of the time. That’s because, and I believe this strongly, Apple never wants 3rd party software to have platform influential power over them again, like Microsoft and Adobe did for decades. It’s sad but not unsurprising that their platforms can be very developer antagonistic if you don’t take their happy path (and sometimes even then). To them though, it doesn’t matter until it affects a large quadrant of the Apple consumer base and in some occasions yes not even then, but largely it’s the consumer who has the biggest voting block with Apple in terms of pressure on the platform, as I’ve watched it play it they never had a history particularly after the iPhone came out of having the best developer relations relative to say, Microsoft, who provides a very positive experience in comparison
It’s just not in their DNA because of the fear of having too powerful of vendors putting pressure on the platform that they otherwise control outright. When you look at their policies in this context they make a heck of a lot more sense (even if you don’t agree. I certainly do not always)
If you wanted something truly private you could create an account at a provider like Fastmail or ProtonMail and create an alias for each account (or just wildcard a custom domain until you need to send from an address). I doubt any tracking system is based on the domain in your email address... not yet, at least.
Facebook auth used to provide an email address, but it's been almost a decade since I last used their APIs so I don't know if that has changed.
Apple's "provide an anonymous email address" inserts them between you and your customer.
Some makers just want things to work and to keep the process as simple as possible for the user.