It ONLY matters for future high-dpi displays.
This isn't necessarily true. Some displays right now are considered to be too high of a DPI for some people.
I know people who cannot read text on your average 17" LCD at the native resolution, whether due to poor eyesight or sitting too far back from the screen or whatever. They could get a bigger display, but that almost always means a higher resolution, so the physical text size on the display is still too small for them.
They work around this by setting the system to a lower resolution: for example, if a display has a native 1280x1024 resolution, they might set it to 1024x768, or even 800x600. (Most of us can't fathom giving up screen resolution like that, but that's what they do.) The trouble is, as anyone knows who's set an LCD to a non-native resolution, everything gets blurred. The LCD has a fixed number of pixels, and it's getting input that doesn't map to those pixels, so it averages a bunch of the data and you wind up with a muddy mess.
Resolution independence solves this problem. It keeps the LCD display at its native resolution, e.g. 1280x1024, but gives them a virtual 1024x768 or 800x600 display. That is, rather than making the LCD come up with the missing pixels, the operating system itself makes the menus, buttons, text, etc. larger by filling in the missing pixels that it knows ought to be there. So instead of text getting blurry, it actually gets sharper, just like changing the font size from 12pt to 16pt would do.
So there are real advantages to resolution independence today. Perhaps not for those with perfect eyesight, but for people who are already struggling with the resolution of monitors, it gives them readability without sacrificing image quality.