Ok, now I understand where you are seeing this. It's an Apple Account email alias, not an iCloud email alias.
I can navigate to the same page. The relevant instructions are here:
About your Apple Account email addresses - Apple Support
Delete an additional email address
- Sign in on account.apple.com.
- Select Sign-In and Security.
- Choose Email & Phone Numbers.
- To delete one of your additional email addresses, click the Remove (–) button next to the address.
Personally, I have two email addresses listed, there is a (–) next to the top one, which is designated as my primary email (which was how I signed up for an Apple Account, a long time ago), but there is no (–) next to the second one listed, which is my @icloud.com email address that I added only a couple of years ago.
I usually don't mind trying things out when helping troubleshoot an issue, but I am not going to try clicking that (–) next to my primary Apple Account email, as I suspect that would cause a huge headache.
So, I'm not sure what to advise other than to contact Apple for assistance.
Genius Bar Reservation and Apple Support Options - Apple
Official Apple Support