How can I erase iPhone when its Apple Account is a nonexistent email address?

It is as Phil0124 says, but if it comes down to it there's the nuclear option:

Apple can completely reset a device if a person can provide sufficient evidence of valid ownership. Check the requirements and steps at: Activation Lock support request - https://al-support.apple.com/#/additional-support Apple says, "Proof of ownership documentation is required," but does not detail what currently constitutes proof other than it “must include the product serial number, IMEI or MEID.” Apple may typically require the original receipt* issued by Apple or an Apple Authorized Reseller. If Apple resets the device this will give you access to the device but won't restore access to the account used to lock it. There is nothing that can be done to expedite an Activation Lock request.

sandman42 wrote:

• The phone authenticates to apple using an email that no longer exists - from a cable ISP which I changed from years ago.

Again, the fact the email account no longer exists has no bearing on the Apple Account itself, they are separate things. The Apple account merely uses the email address as a user name, it is not linked to it in any way whatsoever.

Since my son changed the account ID,

What does this mean?

Did he create an entirely new Apple account, if so, then that again is entirely unrelated to the account on this iPhone. If he changed the email address used for this account to something else then it's just a matter of entering his current password for it, even the new email address is not visible yet. It may just not have updated on this iPhone yet. The password is verified through the Apple servers so should work with the current one, gain if he updated the email address associated with the Apple account.

and the phone only has that ID on it, and he forgot the password used back in December, account management on the phone is not possible.

What password did he forget? The email account password is irrelevant. The Apple Account password which is not tied to the email account is what's important. If he no longer remembers that, then yes you need to request access to the account directly with Apple to be able to remove it.

I think I have (2) options:

ask my son to add the nonexistent email address to his account as an alias, then login using his current password

No, this is neither useful, nor possible. You can't add a 3rd party email as an alias for the Apple Account. It's either the primary email address or nothing at all. Even if you could adding an Alias would not in any way affect the login process to the Apple Account.

• Pursue Activation Lock support request. I have the original sales receipt as an email attachment to prove beyond doubt that I'm the owner.

This may be the best course of action, since the associated email account no longer functions so any password reset emails would be unobtainable.

click here ➜ How to remove Activation Lock - Apple Support

The existence of the email address has no bearing on the function of the Apple Account. You should be able to remove the account by entering the Apple account password for it.

The Apple account and its password are not tied in any way to the email account. The address is just used as the user name for the Apple account.

The elimination of the email account (unless its an iCloud email), does not eliminate the Apple account it was associated with.

You don't need to access the email account at all for removal of the related Apple Account in Settings on the iPhone.

Just enter the appropriate Apple account's password and it should remove the account. Again, it's not related to the email password, though it may be the same if your son used the same password for it.

If you don't know the password for the Apple account, then that will pose an issue, as access to the email address is generally required to reset the Apple account password.