I've only ridden a road bike a couple times and it was smooth for flat surfaces but any bumps... EEK!
Does that mount stay put? Did you like it other than the distraction? Have you ever heard of
these??
The link I gave is a quad lock device but it also includes a case, in that example for an iPhone 6.
The quad lock you listed uses an adhesive to stick something like a cell phone to it if it adheres - read all the exceptions on that list. It also uses zip ties to hold it on.
The one I listed you put the iphone in it (or other cases for other smart phones, or other devices) and it's on the handlebar. The case has a quad lock on the backside and it's very sturdy. It has a locking bucket to keep the mount to the handlebar or stem and is easily removeable by unscrewing the bucket lock. I have yet to put it on my MTB for a test but I don't see a problem. I move quickly in rough terrain so I doubt you would have a problem.
it's very good if you don't know where you are going, and enjoy looking at that stuff.
But I used to race several decades ago even before cyclocomputers were around. And I use very simple ones that show me speed and distance .. the rest I don't need to see. So I put my iPhone in my pocket to track all the data that it stores - heart rate, speed, include/decline, cadence, etc.
I'm never going to race a road race / criterium again but I plan on doing TTs and the bike part of relay traithlons .. I've got my 17 year old bike out of the mothballs to do this and have fun.

Not the greatest of pics but I didn't have the room.
Bikes04-01 - Copy1 by
stevesklar, on Flickr