Why does OS 10.11 require email passwords in two places?

Why does OS 10.11.3 require me to enter passwords in two places Mail and Internet Accounts? I have five email accounts. Only one is with the services shown, Yahoo. I definitely do not use Twitter, Facebook, LinkedIn or any of the other services. I logged on to Yahoo this morning and changed my password. I then changed it in Mail. Shortly thereafter I started receiving notices from Internet Accounts that my password was incorrect.

How does Mail and Internet Accounts interact? For example, if I delete Yahoo Out in the Internet Accounts panel, will it delete it in Mail?

I do not trust iCloud. I have taken Apple at its word several times in the past concerning all of the iCloud antecedents and have been burned too many times. I now only use it for Find MyMac.

When I upgraded to El Capitan, I found I had IMAP versions of all of my email accounts. I do not want IMAP accounts on my computer. I want all mail removed from a server when it is read by Mail on my main computer. When I travel for any period of time, I will manually synchronize Mail, Calendar and Contacts between my main Mac and my laptop before and after a trip and download POP mail during the trip.

How can I get rid of the spurious and unused IMAP accounts in Mail and Internet Accounts?

I do not use Contacts, Calendar and Messages with any of my email accounts.