Why use Dovecot AND Postfix/Sendmail?

MTA is the service that route messages from one region to another. You drop the letter in the public submission box and MTA pass it to the city where recipient live. Then local delivery agent (LDA) delivers letter to the recipient's residence. And then recipient fetch the letter from his personal POP/IMAP mailbox and read it with MUA.

Email simply resembles old good classic mail service. When you get the similarity, you'll get the meaning of each service.

May be that helps

MTA:

LDA:

POP/IMAP:

"Note that Dovecot is NOT responsible for receiving mail from other servers. Dovecot only handles e-mail (a) messages coming out of the local message store, going out to IMAP and POP3 clients, and
(b) messages which have already been received by the MTA and are to be stored into the local message store."

(Taken from http://wiki2.dovecot.org/MailServerOverview)

So there was something obvious I missed; Wikipedia can be misleading:

"Dovecot also includes a Mail delivery agent (called Local delivery agent in Dovecot’s documentation), with optional Sieve filtering support."

Also includes an MDA... Dovecot is, in fact, an MDA.