Just curious what use case this is? Is it that you want to see really important email/texts when you are involved in a setting where having your phone make noises is not preferred?

I have a pebble. It's a lot less disruptive to glance at my watch when something happens than it is to get out the phone. With my phone in my pocket, I'm less likely to fidget with it. And yeah- with my watch vibrating, I can leave the phone on silent all the time. If I want to disconnect, I just take off the watch. It works really well for that.

It's now preferred that my phone not make any noises at any time for any reason. Is there any situation where it would be preferable that your phone make noises?

Once you think of it like that, I think the use case is more clear. It's not about "important" notifications or calls -- it's about all of them.