I think it's an evolutionary thing; during the day, there was work to be done and more dangers about so it made sense to labour and birth in the night where there are people around to support you in relative safety.

Speaking of your body waiting; I think your body can do the opposite as well. I've read stories of women being threatened with an unwanted emergency c/s and dilating very quickly! On the day DD2 was born, DP had an appointment that absolutely couldn't be rescheduled, I was terrified that he was going to miss the birth. But sure enough, she came out with 4 hours to spare!