I agree, that's how they would get married during early Islmaic times, but the question comes, how did the man know this was the woman he wanted to marry in the first place? There must have been some sort of informal meeting by casual encounter, and that in my view is what's lacking in our Muslim communities, specially conservative families.
Of course, the alternative to that is parent involvement (or the auntie-network as Jannah called it in an earlier post), and I wouldn't advise to take this route unless all other ways are exhausted for two reaosn. First, my experience with it is not very positive. It's difficult for parents to know what you are looking for in a future husband. Second, it's even more limited and harder for women. That's because our culture isn't very forgiving when a woman is looking for a man. In our cultures, the man has to show interest first, and the woman either approves or disapproves, having it the other way around is a kind of taboo, something that would bring shame not only to the woman, but to her family as well. I know this is wrong and unislamic, but it's in our culture, and until we have the will to separate unislamic culture from Islam, we'll be sufferring the consequences.