I'm not a fan of the price increase and I don't know if this is the case but I can think of one legitimate reason for the price hike. It is the first price hike since the original ipad. This is the 7th year of ipad sales and no price increases. Sure, some components have gone down in price but newer technology, making components smaller, and figuring out how to shove it into a smaller frame costs money. Add on top of that inflation. Are you paying the same price for a car, food, clothes, etc... that you paid 7 years ago? Okay, that is my most legitimate reason for a price hike even though I don't like it.
It may be the first price increase but Apple has maintained it's already high margins throughout. I doubt this is a case of Apple just trying to preserve those margins because it lowered the price of Air 2, a tablet that shares a lot of the technology that is in the 9.7 Pro. A lot more is shared by the 13" Pro. So much that R&D cost is a lot more diluted than you state. And some newer components might be more expensive but it's washed out by the older ones that have decreased in price.
Ultimately, Apple really didn't make it's own case for the price increase because like everything you noted above, food, clothes, even a car, these are all elastic products. When prices go up people either buy less or buy less expensive items. Same goes for a tablet -- especially a tablet since it's more of a luxury than any of the items you mention. I still haven't seen a good case be made for why the iPad 9.7 is worth $250 (350 if you include a pencil) over an Air2.