I think it's different in traditional Indian families, though, especially those living in India. Granted, I don't think the picture painted in Saat Phere (and other soaps) is representative of all young Indian women and their parents' attitudes, but it definitely defines a certain percentage.
I'm an Indian-American living in the US and think it's important to live a little before settling down. It's difficult at a young age to make such a major life decision, and there's less family pressure here to do something like that. Like you said, growing up is something every woman - Indian or not - needs to do before she marries. I'm not against the idea of an arranged marriage at all (especially now that I'm a bit older and find it so hard to find a decent Indian guy on my own), but I also like the idea of finding someone myself.
Anyway, just some thoughts!