Another opinion from a potential customer (contact centre):
Imagine a scenario where there is no one logged into the system and
email is building up. The email arriving is a mix of urgent, important
and unimportant email.
As soon as the first person logs into the system they should be
allocated the most urgent email, regardless of which email arrives
The second person to log in should also just get urgent email.
Once all the urgent email has been done they should then get the
important email to work on.
Users should not be allowed to "cherry pick" what they want to deal
with, they should just be given a particular ticket which the system
believes is the most urgent.