The term "elective" simply means that you are booked in in advance to have it done. So, of course free elective c-sections exist in NZ as many people have valid medical reasons for having them, e.g. the baby is breech, they have placenta praevia, they've had a c-section before, whatever.
However, if you mean can you choose to have one - i.e. an optional one with no medical reason - then yes and no. Most midwives and obstetricians will not refer you for one, but this is not on cost grounds. It is because a vaginal delivery normally results in a better outcome for the mother, as you can return to normal within a matter of hours, not weeks. But, if your reason for wanting one is that you are bricking it at the thought of having a vaginal delivery, then some practitioners may actually refer you if they believe your fear is strong enough to impact negatively on your labour and birth.
I was booked in for an elective c-section as my baby was breech. She turned herself around at 38 weeks and I ended up having a vaginal delivery. Before the birth, I honestly hadn't cared which way I did it, but afterwards I was so pleased I had had a vaginal birth so that the recovery time was so much shorter. I had an epidural and didn't feel a thing.