It's a lot easier to stay focused when the other guy is focused.
I agree my "focus" comment was a bit offtopic. Got carried away there. :)
EDIT: and I did not say meetings are useless, please don't put words in my mouth. I said don't have them because there are better ways to stay in sync. Meetings can be useful, just not as efficient.
Anyway, this is all getting a bit off topic as far as meetings are concerned. I really think you need to do what is best for you and sometimes that's having weekly meetings, sometimes that's having monthly meetings, and sometimes that's having no meetings. However, I really advocate the weekly meetings, because it's very important to make sure everyone is on the same page. And not to sound corporate or anything, but you need to make sure your goals are aligned.
I also disagree with your long answer. It's not necessarily productive to work in the same room. That's why God invented cubicles! In all seriousness, though, a lot of people -- myself included -- work best in isolation. The bottom line is that you should get the people together in your group and figure out what will work best. Some people prefer working in the same room, some people get distracted because of that, etc. Find our what works best for you and stick to that.