Why should www.domain and mail.domain be used?

It's not only convention. Many email clients (i.e. thunderbird) will try to autodiscover the correct and best IMAP/POP3/SMTP settings based on the TLD with minimal input ([email protected] and password). In my experience, they try mail.domain.tld, imap.domain.tld first until they get a response from a IMAP/POP3 server. Same as SMTP.

Multiple server spanning is one component of the www convention. Another common reason is just that, convention. Some people are just accustomed to typing www before a url now and so, failing to add that subdomain can result in lost traffic. Better to implement it than risk losing some traffic.

And while you may be using a redirect on the www, it still doesn't hurt to have it anyways.