I've had an issue with sign-in with Apple where using an autogenerated emails ruins certain support interactions. One of them was cancelling a subscription service that was eventually resolved (they required me to email their customer support, which I couldn't figure out how to do using the autogenerated email address created by "sign-in with Apple").
Yes but the situation I asked for a solution is different. It is not about not seeing the e-mail, it is about sending from the private e-mail. Example
You subscribe with `private-XXXX@apple-id.com` which relays to `foo@gmail.com`. Customer support asks you to chat with them from the same ID you signed up. Your e-mail client sends email from `foo@gmail.com`. How can you quickly respond to the customer support from `private-XXXX@apple-id.com`?