Thank you BDAqua. That did indeed allow me to get around Apple's screwed up mail configuration software. I actually contacted Apple about this and when they actually saw what I was dealing with, they were totally baffled. With your help I ultimately solved the problem myself.
Note that I was told during the conversation that I was going to have to just "live with it" (i.e., use iMap configurations) since Apple was also moving toward no longer supporting POP anymore (news to me!).
Re: your other question as to WHY use POP, I guess there are several reasons. My HD just crashed and my iMac is in the shop awaiting a new SSD :-) so for the week I'll be without it, I thought I would set up access to my account via my wife's iMac that uses the same OS and version of Mail. I have used the POP account at Earthlink for over 20 years now. It was while setting up the new account on my wife's machine that I ran into the issue with Apple's Mail software.
My work flow is such that most of my emails get shuttled off to other mail boxes in my Mail client. I have over 50 of them and I do get into each of them on a regular basis. Since I run my own backups on my iMac, I am in control of ALL of my email history. Also, by doing things this way I never have to worry about running out of space on the iMap server (many of my emails contain technical diagrams and attached documents). I can also get to those emails for reference even when the internet or my mail servers are down.
Also, on my iPhone 5s, I'll got very little screen space to work with and trying to support 50 mailboxes in the Mail client there is very difficult.
Although I was able to set up a POP account now on my wife's computer, since this is temporary, I changed it back to an iMap configuration to see how things go. When I get my computer back, I'll decide then how to move forward.
Thanks again for the assist!
