There's sapphire watch faces for hardness, and sapphire substrate for semiconductors (https://en.wikipedia.org/wiki/Silicon_on_sapphire)
They could even create the equivalent of a "perfect pixel" guarantee - "perfect lattice" guarantee, the diamond screen is flawless down to the atom or your money back.
That could flip the script on DeBeers in a big way.
[1] https://www.technologyreview.com/s/532636/why-apple-failed-t...
Now, that doesn't necessarily mean that a diamond screen would be worse than what exists today but it wouldn't be something invulnerable and resistant to any impact either.
The predecessor to your phone, my Nexus 5, also contains Gorilla Glass 3, and yeah, I don't use a case, I don't use a screen protector, and there are no real scratches on the screen, and it has rode around in my pocket for over 2 years.