Being the RegF officer in the RSS position, I can tell you it's a constant internal struggle to decide whether to send an email to a members' civilian or military email.
I'm used to quick responses and quick turn arounds in the RegF, and I've really had reign myself in to learn to decide what is and isn't time sensitive, and stop and think how/when to send emails out to the Class-As.
For routine business, if it can wait two or three days until the department heads and divisional officers are in, I will send it to their military emails, even if it means I can't finish a task right away (which is hard for me, as I'm the type that likes to get a job done right away). If it can't wait 2-3 days, then I will send it to their civilian emails. When it comes to my command team (CO, XO, Coxn), my emails almost always go to both their civilian and military emails, as they want to be informed immediately of everything going on.
That being said, I do agree that we really way too heavily on civilian cellphones and email. Sure, senior staff have sort of signed-on to be plugged into the business and can be expected to be more available, but what about our junior sailors and soldiers?
It may seem unusual to most, but there really are soldiers and sailors that cannot afford a good cellphone plan. This isn't the regular force, so they don't have a guaranteed income. We have sailors who's only source of income is their Class-A work and don't have reliable data plans, yet we still chomp on these people to respond quickly to emails from their chains of command, and I just don't think that's fair.