I believe too one should be able to set POP to delete messages from server.
In fact it worked pretty well.
However, it worked only with email account providers which do not have anything in common with Gmail/Googlemail.
For that of Gmail or those based on it that did not work!
However all those attempts were made in the past and with other email client than os x's Mail.
Two rules were set for each new message:
- fetch it from server
- delete it on server
Locally on client side all looked well. One day few months later after had started doing so a short look into account
using the web email client shown it is not true - all the mails fetched earlier reside still on server. How an frustration!
Because with this it turned out one needs periodically to log on to server via its web client and do the cleanup,
the used model means server is slave and is allowed it keep messages till those are not fetched by master client.
The general recommendation that time read change to IMAP in order to achieve the aimed goal.
Now all the accounts are set to imap under Mail.
IMAP has some other advantages: if one day on slave client a email template or draft should be done,
it is easier to transfer it to master client. The same if one day a rare case should occur that from slave client
an email is sent.