Same here. The address I am adding used to be my Apple ID. Wonder if a record of it somewhere is causing the issue.

I've noticed it as well. I tried many aliases. My family however could create email addresses on the domain I added. The issue seems to be with my account rather than the email addresses I try to add.

Is your Apple ID a third-party email or one of the @mac.com, me.com or icloud.com domains? Mine is third-party. I changed it a few months ago to a third-party email. I noticed I cannot save drafts or send from my original @me.com email address which was also my original Apple ID from iCloud.com/mail/.

I don't have this setup. My App Store account and iCloud account is linked to the same Apple ID. My family (Linked via Family Sharing to my account) can create custom email addresses no problem, just my account. Apple Support was no help.