I have to agree with the software developers.

My company provides IT support to various other companies and organizations and we have a service goal of responding to emails within 15 minutes. Now, I work in the office so I'm not directly part of support, but it is my responsibility to see that those emails are answered. Even if all I can say is that someone else will be checking on them/creating their username/fixing their problem at such-and-such time.

My work around has been to answer those emails as they come in and move other items, such as requests for reports, to an @action folder that I go through an hour before lunch and an hour before leaving for the day. Things that are in @action but will take a while become the first thing I handle the next day or I schedule it in my hard landscape.

When I need uninterrupted thinking/working time (thinking reconciling accounts or preparing company tax reports), I make sure that some other person knows that I'm going to be out of the loop unless needed. I delegate the responsibility to someone else. Along the lines of setting an appointment for myself, only instead of saying I'll be out of the office for a meeting, I tell them that I won't be watching emails and I'm forwarding my phone for an hour or two while I untangle whatever mess I'm working on.