The only time we have use the admin user was when we have installed Moodle. After that everybody got is own account and if you need admin privileges we upgrade the user to site admin.
We were thinking to disable the admin account but we realise that email from that account will be block. Then I found this thing :
I think that exactly what we want. To keep the admin account active (because we don't want the main admin to be a specific person but generic account) but to have nobody be able to log as this account.
Do you see any problem putting the "no login" authentication for the admin account ?