Many web sites and apps do not use Sign in with Apple. And they could block the domain for account creation with email without blocking the domain for account creation with Sign in with Apple. This would not make sense unless Apple changed what personal information Sign in with Apple provided probably. But they could.
I think you as the user can use the aliases without Sign in with Apple though, right?
But otherwise, you're right, any website that wants to accept Sign in with Apple will almost certainly be agreeing to Apple's TOS for Sign in with Apple I presume will stop you from blocking this service.