There are over a dozen hardcoded references to both the External ID of this account "based.admin_user" and to the database ID of this account "2".

This user is critical for the successful operation and administration of Odoo.

Without it:

• you eliminate "superuser" access, potentially locking you out of key admin functions.
• you risk breaking automated actions and scheduled jobs.
• you introduce potentially critical data integrity issues - resulting in errors in logs, incomplete record history and the inability to track user actions.

Recreating a user with the same name or email as base.user_admin does not restore the original superuser privileges.

Even with elevated permissions, such recreated users lack the id=2 association that we use for superuser identification.

We have even gone so far as to prevent the ADMIN user from being deleted via the UI.

Hi, You shouldn't delete the admin account because it will cause you a lot of grief but you could archive it if truly necessary. You could simple rename the account, reset the password, and give the new credentials to the new administrator.
Without a complete understanding of your scenario, if you are determined to follow this path, as the current administrator, 1) create a new or use an existing the account 2) allow the new account "settings" permission (this gives full admin rights, 3) ensure you can administer the system with the new account, and then 4) archive the current admin account. 
Hope that helps you out.