Re: short sighted
A simpler method would be to learn how to manage your email more efficiently.
Agreed. Start with switching from an interrupt model to a polling one, by turning off notifications and deliberately only looking at email at scheduled intervals (e.g. only at the beginning and end of the work day).
Of course, you can do the same with most messaging systems. When we started using RocketChat, the first thing I did was turn off its notifications. Now it's essentially just another email MUA for me, and I go through the messages once or twice a day.
I still allow notifications from Lync / Skype for Business, as they only come in rarely. If they became bothersome I'd disable those too. If there's a genuine emergency they can always phone.
I can't disable Fuze notification popups (Fuze sucks, frankly), but I can, and have, turned off the sound for those, and they don't steal the keyboard focus, so they're not too bad.
When I were a lad, I interviewed for a job at a smallish software firm whose flagship product was a time-tracking system for lawyers and other bill-by-time professionals. They had a firm policy: between 10 AM and noon, and 2 PM to 4 PM, developers were not to be interrupted except for emergencies. Email and phones were off, and meetings could not be scheduled during those blocks. I suspect it was not a bad idea.