There was a lot of debate about this when iPhone 4 first introduced Retina, but when laser printers made the jump from 300DPI to 600DPI, the printed text looked notably better, even if one's eye can't really detect individual dots at 600DPI....
The laser printers could only print dots that were either 100% black or 100% white. So if you want to print text that has a gray level of 75%, you need to print three black pixels, and one white pixel, while your iPhone or any old LCD monitor just displays a gray pixel. So you need a lot more resolution on these printers for the same result. Twice the resolution (600 dpi) just to create five levels of gray.