OP, good question! I've been thinking about this a lot lately, ever since the topic came up on another thread a few days ago.
IMO, If they were really concerned about modesty, I don't think they'd insist on the gowns! I feel much more comfortable in my own skin than half-covered by one of those ridiculous things. But people (especially in this culture) are funny about other people's nakedness (just think of all the stories you hear about new moms being harassed for NIP), and I think the nurses sometimes feel that if they're uncomfortable with it, you must also be uncomfortable.
I remember that in labor with my first, at some point during pushing I realized that it would be hard to nurse the baby immediately while I was wearing a bra. So I took off the bra and pulled it out from under my shirt. It got caught up in my IV, though, and was just hanging there next to my bed. I couldn't have cared less, but the nurse got all clucky and said, "oh, we don't want that flapping in the breeze!" and went to a great deal of trouble to whisk it away. I just looked at her like, "are you serious??? I'm lying flat on my back on a bed, bared to the waist, with bodily fluids everywhere, and I'm supposed to feel embarassed because somebody might see my bra lying around???" *Shrug* So who knows what that's all about, really?
Honestly, I suspect it has to do with all the "what-ifs" that are always front-and-center in hospital staff thinking -- they're worried about having some crazy emergency where they have to cut your clothes off to get access to some odd part of your anatomy, and they don't want any complaints from people later about them destroying clothing to get there. That also seems silly to me, but I wonder if that's part of it.
Of course, "Birth is a messy process" is certainly true -- if you wear a hospital gown and it gets messy, they can just toss it in the bin and get you a new one -- they don't have to keep track of what you were wearing and set it aside for you for later. And if it has blood or something on it, it's probably considered a biohazard, and they probably have all sorts of weird rules about handling it. So they want you to wear a gown because it ends up being less work for them.
And then, there's always the symbolic meaning of having a laboring woman dressed as a "patient." There's a fascinating article here: http://www.terrylarimore.com/BirthRites.html that has quite a bit more on the topic.
I never wore a hospital gown, personally, and I don't intend to this time, either.