The engine doesn't "want" anything -- not a Cherry Coca Cola Slurpee, not a cigarette, not a pot of gold, not a pot of chicken soup, and not to idle at 580 rpm. It's idling at 580 rpm because the speed is not properly adjusted. The correct speed isn't arbitrary; it's what happens when all the relevant adjustments (idle mixture, ignition timing, idle speed screw) are set correctly, and the result is that everything works optimally in terms of how the car starts, runs, and drives. That's not arbitrary (or random, or magic), it's just how it works. The carburetor's idle transfer port and vacuum spark advance port are in very specific locations relative to the throttle plates, for example, and everything's calibrated based on the throttle plates being where they're supposed to be. You've got some lattitude, of course; it's not like the car won't run (or will run like crap) if you don't hit the spec dead on target, but 580 is far enough below where it should be that there are going to be problems—some of which are already mentioned (line voltage droop).
I imagine the idle speed specs are an average recommended speed
