I think it is a key skill. My DH lived on the edge of London as a child and never learnt to drive "because he didn't need to". However, he then wanted me to take him places in my car - sports stuff, supermarket shopping, visiting people, the list is endless. He even asked me to drive him somewhere when I was pregnant and very ill with hyperemesis - I could barely walk, let alone drive and he made a real fuss about it.
So, I taught him to drive myself and asked him for £4k and went and bought him a small car with it. Now he drives when he needs to and it is so much easier - he admits he was totally in the wrong relying on others all the time and loves the car I chose for him. It has left us with a residual difficulty - because he is a new driver, he is not confident (and neither am I TBH!) enough to take my 1yo and/or my 3yo anywhere without me ever. After giving birth both times, I had to be driven home from hospital by my mum.
It is a key skill for both sexes. OK, don't own a car if you don't want to. However, do consider getting a licence. My licence (and insurance) got us out of a sticky situation one night when we were younger - we had accepted a lift from a friend somewhere about 10 miles away one evening and he proceeded to get very pissed and then say he would be driving everyone home. As I hadn't had anything to drink, I was able to drive everyone home in his car. Even if we had said OK we will walk the 10 miles home in the freezing cold & dark, another friend (also drunk) would have got in the car with the would be drunk driver. This "drunk driver" was a responsible, very religious teenager and I did not expect this from him at all. But at least I had a licence and my own insurance and could solve the problem for everyone.