This is an interesting thread because I've been having some of the same thoughts on independence.
Well, brother, let me tell you that I live alone and I love the independence and privacy. I had the same thoughts as you: I gotta get an apartment or else I'll look like a loser. I went through college by myself (no parental help) and now I have had my own place for over 2 years. I'm now 24. I was so proud of myself for being on my own and I thought it would really help me with the ladies. But let me tell you something:
It didn't. Not one bit.
I've actually been trying to get this kind of opinion out of women I meet. I got my hair cut by an attractive girl the other day and I asked about this very thing, whether having your own place is really necessary for attractiveness. The answer: a lot of girls really don't care if you live at home because a lot of THEM do it too. She lived at home herself and so did her b/f.
So let me tell you something you probably didn't think about that a lot of these posters are hinting at. There is something more important than independence when it comes to women: money. I might be on my own, but I can barely afford it. I have NO money. Ever. I can't even by decent clothes or fix my car. So when I approach a woman the first thing she's going to notice is my physical appearance complete with ratty clothes and shoes and my old, broken possessions. I might have "independence", but I look like a beggar. I just don't have the "financial independence" that I really want.
Think about it this way: When will a girl learn you live at home? AFTER the first impression. When will a girl learn you have no money? Immediately.
Apartments are expensive, man. No lie. You will be saving hundreds of dollars a month living at home. That's money you could be putting into other things that will improve your odds with women. If you're only 20 that's no problem at all. That's becoming the standard. When you hit 30 though, you better get your ass in gear.
I'm struggling terribly to pay my bills. The people I know who lived at home (and still do) are MUCH better off than me in terms of money and relationships. They can save for homes and cars, they can take their women out to nice places, and they are much more care-free than miserable old me. Girls really don't seem to care, man, honestly. And it's really been pissing me off. I really thought this apartment was a good selling-point, but it's only a cool little bonus. Stay at home, save your money, and improve yourself in other ways that will improve your odds. Independence is over-rated and over-priced.