Did you read the article? It seemed very clear to me that they had significant issues with customer support past just verification.
And what would you suggest as an alternative way to identify the user, anyway? Any alternative method of authentication seems doomed to fail - using a real name runs into issues with duplication, requiring users to set a username would likely require significant changes to the platform to support it and lots of people would forget it when they couldn't get their preferred username, and having a customer support code inside the app wouldn't help when the user loses access to their account.
It seems like there are alternatives, but none that the average user who signs in with Apple and needs to contact support will be able to get past on a consistent basis.
I actually think the customer experience of "I switched from apple to android and now I dont know any of my usernames" is a bigger issue. If apple wants Sign in with Apple to work, it needs to behave a bit more like an agnostic 3rd party password manager, work on every platform, and have ways to interact with it on any device. They should release Keychain as an Android app and Chrome extension, and allow you to use it to see your Sign in with Apple data.