When I was a desk jockey, no. I separate my phone and my keys and I don’t use cash (no coins in pocket). Now I move around a lot more at work, tend to carry more things and have increased the risk of dropping my phone so that feel like it is necessary now.
That's kind of contradictory. The oleophobic coating is naturally organic, which wears off eventually as it is. So it's meant as a basic layer of protection, which if you add a screen protector, you're not really taking advantage of the oleophobic coatings purpose.
My family has had 10 iDevices including iPhones of 3GS, 4, and 6 and we have never scratched or broken a SINGLE ONE of the screens. We typically use iPhones for at least 4 years before replacing (typically for OS feature or security reasons). I also support iPhones at work and have only seen one broken screen out of hundreds of iPhones over the past five or so years. Unless you are carrying hardened drill bits in your pocket or are really grinding sand into the screen then you will not scratch your iPhone.
A good case that has a lip to protect the screen in case of drops IS a good investment. But all of these screen protectors have not been useful since the Palm Pilot went out of style.
And those hairline scratches are almost impossible to avoid. Even using a clean microfiber cloth and wiping down the display, it's still can accrue those very minuscule tiny scratches that are only visible what the reflection of light on certain angles on the display.
I've never used a screen protector on any glass screen phone. Never had a scratch. But I also never lay it face down on tables, and I keep it alone in my left pocket w/ no keys etc.