Given two displays with identical dimensions, where one has twice the DPI of the other, then a square specified to be "width: 400px" should be physically half the size on the higher-DPI screen.
Designers who want to render at a particular size (e.g. for buttons that a user will push) should specify sizes in physical dimensions, such as inches or cm.
What about the fact that we have dpi's going from 250 to 450, everywhere in between? We have color temperature problems, we have totally different screen aspects sizes. Between all the things we can't control, why is it still a good idea to render with pixel accuracy?
Designers who want to render at a particular size (e.g. for buttons that a user will push) should specify sizes in physical dimensions, such as inches or cm.