I originally moved out freshman year of college. It wasn't shocking or jarring at all. Though it was better a couple of years later with my first apartment so that I could cook for myself instead of having a meal plan, because those were ripoffs.

In my case though, I'm not really cut off from my parents. I've yet to find a job on or near campus, so my Mom is still handling things like my groceries, admittedly. To say I'm "independent" would be silly considering how much I'm relying on her still.
This is pretty typical for young college students. My freshman year, I would sometimes add some money to my ID card to use at various college-run meal outlets, and the person I dealt with inevitably expressed surprise when I handed them cash. Apparently most kids just sent the bill home to their parents.