Because many sites check the domain part of your email address against a blocklist, which contains entries like trashmail.com to prevent users from signing up with ad-hoc throwaway accounts. They don't want that, because they'd like to get a proper lead they can either track, sell, or reach out to.

Now Hide My Email allowed you to do just that: Create an account with an email that wasn't tied to your identity, and that you could just decommission if you didn't need it anymore. Sites had no way to detect these either, because all of the randomly generated addresses Apple provided you with just ended in @icloud.com, which is also used by tons of regular accounts - so if you blocked this domain, you'd invariably preclude millions of people from your service.

But by separating the domains, sites can simply add private.icloud.com to their trash mail blocklist, preventing the use of Hide My Email, while regular @iCloud.com addresses will continue to work. It makes the entire service useless at once.

But that will completely break Sign in with Apple, which no service is ever going to do. I really don’t get the problem here.