"There is no reason for a larger screen to require 551 (or really any specific) pip"
You do know that every increase in screen size Apple has ever done on the iPhone/iPad has had a ratio of exactly 1-to-4 pixels, right? There is a specific reason for this.
iPhone 3GS -> iPhone 4
480x320 -> 960x640 (exactly double the height and width, and quadruple the total # of pixels)
iPad 2 -> iPad 3 retina
1024x768 -> 2048x1536 (exactly double the height and width, and quadruple the total # of pixels)
iPad Mini -> iPad Mini retina
1024x768 -> 2048x1536 (exactly double the height and width, and quadruple the total # of pixels)
iPad -> iPad Mini
1024x768 -> 1024x768 (exactly the same height and width and total # of pixels)
The reason they do this is because for every square pixel, you now have 4 smaller square pixels that can perfectly represent that original 1 square pixel. This requires little to no work to make old apps function and look good on the new display. If instead, you had something like 2, 3, or 3.6 pixels for every 1 old pixel, then the pixels would no longer perfectly match up and unintended adjacent pixels would be filled up to try to match the original pixels as closely as possible (though it wouldn’t be able to produce an exact match as it can with a 1:4 ratio), which would cause icons/graphics to look blurry and ugly, and could also cause problems with touch input precision.
If you don’t adhere to that ratio, you get icons that essentially look like this:
Image
This is the reason why a lot of Android apps look ugly / unoptimized - because apps are not optimized for a specific number (or ratio) of pixels for each Android phone.
This is also why if you download a retina iPhone app to an non-retina iPad through the app store (which have a different ratio of pixels, 1:1.28 to be exact), it will show black bars around ALL 4 edges to match the pixel ratio, because if it was to expand to reach either the top/bottom or sides of the screen, the 1:1 ratio would become a 1:1.28 ratio and the pixels would no longer line up, and blurriness/ugliness would occur. Apple prevents this by enforcing black bars all around the app and preventing full-screen upscaling.
If they don’t follow the 1:4 pixel ratio and choose a random/arbitrary/different PPI, every single app developer will have to make a choice as to whether or not spend the time and money required to update all their graphics/images/icons to the new PPI to prevent them from looking ugly/distorted/blurry on the new display. And considering it took many developers (including high-profile ones, like Google and Rockstar) very long to simply update their apps to the taller iPhone 5 size (and there are still some apps that haven’t updated to the iPhone 5 size yet, 1.5 years later), a much larger change requirement of re-mastering all images/icons/graphics used in the app would take even longer and may show a negative cost/benefit for some developers. Additionally, Apple itself would have higher costs in updating all the graphics in their own apps as well.
So if Apple were to maintain the 1:4 ratio by doubling the height and width again from 960->1920 and 640->1280, and trying to fit these pixels into a 4.7” diagonal screen, then the mathematics dictate a required screen PPI of 555. Screens with such high PPIs don’t even exist yet on the market in any mass-produced consumer electronic device due to their high cost, making a larger screen size for the iPhone 6 very unlikely.
Resources:
A Programmer Explains Why Android Apps Are Ugly - see section titled "Dealing with screens of every possible size"
Why Are Android Apps Ugly? - see section titled “Writing for multiple phones”
Why do apps from the same company look worse on Android than on iPhone?
Why is the general UI in most android apps ugly?
https://developer.apple.com/library...s.html#//apple_ref/doc/uid/TP40007072-CH6-SW1 - see section on App Icons and Launch Images
http://en.wikipedia.org/wiki/Image_scaling
http://en.wikipedia.org/wiki/Aliasing