I don't know what the percentage is here, but no one at our hospital was surprised by my choice for natural births. In fact, the nurses there were so busy trying to read and accomodate my birth plan (I arrived late for the second birth) that they almost missed I was in transition!
Likewise, none of the nurses were thrown by following the birth plan, and none of them were surprised by an alert baby. They seemed to expect the baby to be alert, and were right there to work on a proper first latch.
This was at a pretty traditional hospital, in a large midwestern city...no midwives practice there, and as far as I'm aware they don't even have labor tubs. Even so, natural births feel and seem like a very normal occurance there, and nurses are totally comfortable with it.
...Heck, even with my twin birth (which was also natural), the anesthesiologist came in and practically apologized for being around because my birth plan said I didn't want pain medication. He had to be there in case I needed an emergency c-section (ds2 was breech and both boys had heart issues), but after introducing himself (and acknowledging my birth plan), he backed way up into the corner of the room and was respectful as can be.
So even in the most traditional pockets of America, at the most normal hospitals, you might be surprised!