I don't see how sapphire would make it thinner
I was just speculating in an effort to try to justify an answer to "Why Sapphire (vs. Gorilla Glass)?" My guess there was that since Sapphire is dense, maybe that pane could be shaved a bit thinner than a glass pane and thus contribute to overall thinner design goal. After all, once something gets down to being measured in a few millimeters, ever little bit of shaving contributes.
Personally, I'm in the camp of "when is thin, thin enough?" as I think continuing to make iPhone thinner and thinner starts losing something. For example, where does it stop? Does anyone actually want an iPhone that is as thin as a sheet of paper? While that might be cool for a moment, the day-to-day utility of just picking it up might become an aggravation (not to mention structural integrity of being in a pocket and what would seemingly be miserable or impossible battery life tradeoffs).
"We" have somewhat conditioned ourselves to expect "thinner." Like any rumor that goes from rumor to "very likely", "we" tend to get behind anything we expect from Apple. For example, hop backwards a bit in time and any phone with a screen bigger than 3.5" was an "abomination", "need new pockets", etc. Then the 4" was rolled out as the new and perfect size and any phone with a screen bigger than that was tagged "abomination", etc. Now, 4.7" has crossed the bridge from early rumor "abomination" to very likely and the crowd is shifting into liking it while still poking negative at bigger.
I think "thin" is very much that same thing. Since we're used to Apple spinning "thinner" every time, "we" expect the next one to be thinner so "we" mentally like the idea even if we personally think the current one is thin enough.
So, if Sapphire is about thinner, I'm personally not excited about that at all. For that slight thinning, the replacement part will probably cost quite a bit more for those who have an accident. Unless scratching screens is a big deal to some, I'm not seeing it. Maybe there's something to Jvanleuvan's post about 3.3 times more shatter resistant? If so, THAT would be a big deal. I just haven't seen that anywhere myself until his/her post. If it could cut the shattering pain by some meaningful level for users, that could definitely make the case for the switch.