Anyone saying Apple is doomed...well aside from the obvious one, it is someone who clearly isn't paying attention.
The real question is if they'll maintain their profit share dominance.
They don't engage in the DPI race because it largely makes little difference to go past where they are now, and have been since the iPhone 4 (excluding the 6 Plus weirdness).
They were the first to do high DPI yes, but they didn't kick off any "race". They took their displays to the DPI that they thought was necessary, right to the point where the slope on the diminishing returns curve becomes exponential. The Android OEMs desperate to differentiate themselves started the "race".
No, it is because they locked in production and aren't willing to lose margins to keep updating some components every year. Has absolutely nothing to do with it being "optimal" (or else we'd still be locked in at the 3.5 or 4 inch display sizes after all). It is the same reason they actually downsized the batteries, so they can maximize profits. So yeah it is optimal in that regard.
I really don't know how you can claim that they're not playing the DPI race considering how they've been upping DPI on their products in general (they just released a 4K 21" iMac for crying out loud, yeah, they're not playing the DPI race at all...). They were absolutely not the "first" to do high DPI either, they have however been explicitly marketing high DPI ever since though, which is why Android has been pushing it as they trump Apple's "Retina" displays in resolution.
It's funny some by now still don't understand the concept that raw spec increases like DPI doesn't necessarily means an equal gain in real world utility, and the latter is what ultimately drive demand not the former.
Funny how some people can't see what is plain. If that were truly the case we wouldn't see companies intentionally ditching utility. Even Apple themselves when they decreased the size of the battery despite battery life, especially over time being one of if not the biggest complaint about smartphones in general and the iPhone especially. There's very obvious reasons for that, and it is partly why they brought out the + and I've seen a lot of people who don't want the larger phone (tell me again how a phone with the +es bezels is somehow "real world utility"?), but they get it because of the better battery life alone. Real world utility, I guess that's why the iPhone's have quick charger too. Oh they don't? Weird, I thought real world utility drove demand. Much like how people have been saying "I don't want or need more storage, 16GB is plenty enough, especially for shooting 4K now!"