I recently experimented with an app called Moment which tracks how you use your iPhone. It will show you a running total of minutes you've been on your phone for the day as well as where you use your phone. I first tried the app a couple weeks ago and after an unusually light morning of phone use (I had only used it 15 minutes over the course of 3 hours) I decided to see if I could make it the whole day, using the phone for less than 1 hour. It definitely wasn't easy and at the end of the day I had used my phone for 64 minutes, so pretty close to meeting the goal but it illustrated a few interesting points. The first was a recognition of how much time I am "using" my phone without actually doing something productive on most day, as well as how unbelievably efficient you can be when you consciously decide not to waste any time when using the device.
If you subscribe to the theory of Parkinson's Law which basically says that work will expand to fill the time allotted to complete it, then you should be able to make that work in reverse. We know that the average worker is only productive for a fraction of time they are actually at their place of work. The smart phone has become a similar environment as you notice you've been holding your phone in our hand for the past 20 minutes but haven't actually done anything with it.
So while it may not be logistically reasonable to only use your phone for an hour each day, as an experiment it's very interesting and also trains you to get into productive mode the second you start actually using your phone. Try it out and leave some feedback in the comments.