People do give birth alone or with just their partner with them - it's called 'free birth' or 'undisturbed birth'. Some women choose it but I wouldn't recommend it as a midwife, obviously.
Some women experience orgasmic childbirth (there's a documentary about it, and I've met several women who have). Women don't usually describe orgasmic birth as sexual, though. It's more sensual, or orgasmic in a different way that's not really about being with a lover.
Some women do find kissing and nipple stimulation to be great for pain relief in early labour, and to increase oxytocin levels that helps stimulate uterine contractions and make for an efficient labour.
Birth is a powerful act of creation, an embodiment of a woman's sexuality. It is the culmination of a sexual act, it definitely has many sexual elements. Understandable that it's the object of a fantasy. I have spoken with many women who felt incredibly powerful while they were giving birth, and it can be seen as a sexual power - a reproductive, creative power.