I have a similar problem.
We tried to set up new (first time) Apple ID on a new device. It would not accept the email address domain name, which is a personal one, but perfectly valid. We tried to setup an iCloud address separately but that wouldn't work because we had no means of verifying it.
We had several goes and then decided to use another valid email address from a mainstream ISP. That worked and then became the Apple ID, so we then were able to create an ****@icloud.com address as a username alias. Then we found the same problem as you other guys - we cannot delete or separate the alias or original ID.
We are not talking about email contact or alias addresses. Other than the two created in the login process, others can be freely added and removed for contact or email account purposes.
Now I am stuck - the mainstream domain adddress will forever be associated with Apple. Customer services have confirmed that it is impossible to remove an Apple ID (whichever address is used to create it) or remove any ****@icloud.com addresses or aliases.
It stinks.
To add insult to injury, after trying desparately to right this mess, Customer services then enabled my private domain name so that it could be used for a primary Apple ID. We have done that now and are using an alternative ID, but the icloud address we created is being used as an alternative contact address so the originally created ID thinks we are logged on as that, as well as the alternative ID. If I had realised that I would be in this mess and that the domain could be enabled, then I would have called Apple first and we would have been OK.