So Blogger changed the possibility, with Blogger Beta. Under Beta, you can add a second (or third, or ...) adminstrator, but you can't delete the first administrator. That takes care of the possibility of having no administrator. But it creates a second problem (which apparently Blogger doesn't find important) - you can end up with an account that has no need to administer a blog, but having been the first administrator, is stuck with that ability none the less.
Having accepted that fact, one bright person came up with the idea
OK, what if I delete the first account?
A drastic, but seemingly effective way to resolve the problem.
But today, it appears that procedure is both drastic and fatal. When you delete the original administrative account, the blogs associated with that account disappear. This is stated by Blogger Employee, in Blogger Help Group: Something Is Broken Since switch my blogs aren't on dashboard Help blogstars or Employee.
...the problem appears to be that you deleted the Google Account that these blogs were registered with. Be aware, when you delete your account, your blogs go with it.
In other words, do not delete an account having any blogs associated with it.