I've repaired a couple iPhone 6 screens for less than the cost of an AppleCare incident deductible. iPhone 6 Plus, on the other hand, is ridiculously expensive to repair yourself.
I probably have far more dropped calls but it's because of that damned MicroCell at my mother's place.
I'm surprised that you wouldn't consider the Spigen Slim Armor "robust." I had a Spigen Slim Armor for my Samsung Galaxy Note 3 and it kept it in flawless condition while adding a bit more bulk than I wanted. No doubt, it wouldn't have protected the screen in a drop where something hard directly contacts it (like a rock; what would?), but at least it raised it so that the screen would not impact on a flat surface. The case's plastic shell got an invisible crack above the volume keys due to taking it on and off, but it did its job and protected it through a few drops. I did have a screen protector film applied too.
I actually felt that it was too much protection (borderline Otterbox). Impacts usually only do cosmetic damage when a phone falls on the back side so a skin and a bumper frame should be more than enough. Once again: not much you can do about protecting the screen without a belt holster or something covering it (Slim Armor View comes to mind).
When I got my iPhone 6 Plus I used that logic and switched to a Spigen Neo Hybrid EX Metal bumper case and an Armor Guards Military carbon fiber style protective skin over the back. I used that with the included Spigen screen protector until I could no longer tolerate the reduced signal strength (aluminum blocks cellular and WiFi signals). The Spigen bumper did include a clear film protector for the back as well but I wanted the phone to look black front and back like my leathery Note 3. I loved how it looked and felt: minimal and sturdy until you drop it and bend the frame (easy to straighten once you know how to get it on/off the right way). Even if I couldn't fix it, that's it's job, to take the brunt of the damage in place of your phone, right? The Space Gray aluminum bumper looked so much like the naked phone that I never felt like taking it off to handle/view my phone without the case, but the signal issue eventually led to me dropping it on the pavement naked (removed it to maintain a signal). Grrr.
I eventually switched to the plastic version of the Spigen Neo Hybrid EX and found that it was noticeably thinner and that the ringer switch was much harder to access through the smaller opening. I see mention of it having been redesigned since launch so I'd be interested in seeing the older version. The plastic frame from my EX does not fit the TPU from my EX Metal. I loved the leather feel from my Note 3 and the SGP leather skin with logo cut-out that I had on my old iPhone 4 so I switched the carbon fiber skin on the back to a $3 faux leather one from China. It feels like hard plastic. I did protect the Apple logo cut-out by applying the carbon fiber logo pieces left over from my Armor Guards Military skin. Both were cut exactly so it's a perfect fit and looks pretty cool. I was going for that "this is what a black, naked, iPhone with a leather back would look like," look. The leather skin actually wraps around exactly as much as the display in front, which makes it look like a black phone with an aluminum frame (the naked look I wanted in the first place). Admiring that outside of the case meant dropping it on pavement without a case and marring up the edges.
Obviously, the Slim Armor's additional bulk didn't protect your screen, but neither would an Otterbox. There's no reason to add even that much bulk to get similar protection: a bumper, a skin, and a screen protector is fine for most phones... unless you have the Galaxy S6 with the glass back that shatters, skin or not.