How do I remove a 'contactable at' email address from my Apple ID?

Add and manage email aliases for iCloud Mail on iCloud.com - Apple Support

"Note: You can’t delete or turn off a primary iCloud Mail address. You can’t use an alias to create a separate Apple ID, and an email alias can’t be converted to a primary iCloud Mail address."

From About your Apple ID email addresses - Apple Support

Additional email addresses

Many of us have more than one email address that

friends and family use to reach us. You can add additional Reachable At

email addresses that you commonly use to your Apple ID account, so

people can easily find and communicate with you on Apple services like

FaceTime, Messages, Shared Albums, and Find My, and collaborate with

Pages, Numbers, and Keynote.

Delete an additional email address

1. Sign in to appleid.apple.com.
2. Select Personal Information, then select Reachable At.
3. To delete one of your additional email addresses, click the Remove button  next to the address.

Apple hasn’t published any guidance for using an address again. Normally, if your e-mail address was associated with an ID in any way, for example as a Notification email address or a Rescue e-mail address, then it can't be reused as an  Apple ID email address for approximately one year. I have also seen posts that stated Apple told them there was a 30 day waiting period before the address could be used again. You will need to get another e-mail address from somewhere like AOL or Yahoo to use as your Apple ID or you can try waiting 30 days to see if that works.

Based on what I have read, I suggest you leave your Apple ID email address as a 3rd party email address because you have more flexibility if you need to change the email address. For example, if the Apple ID got compromised, you can change it to another address. I also have read of many people who were locked out of their accounts when they forgot their password. Since the recovery email address is the @iCloud email address, if you forget your password, you also can't access your email to get emails from Apple to recover your account. You can set a rescue email address, but for some people, this hasn't worked.

According to About your Apple ID email addresses - Apple Support

rescue email addresses no longer exist if you're using two factor authentication.