Cars are not a good analogy for this situation, at all. The presence of software and computers in our life is much closer to the invention of the alphabet and writing. Written text gradually becomes so ubiquitous in life that being illiterate is a serious handicap for anything you want to do.

Likewise, the amount of software and technology we deal with on a daily basis is increasing at an exponential rate. It is just a matter of time before the ability to deal with it at a deep level becomes a necessity of life.

Of course, not everyone will be paid to write code, just like not everyone is paid to read/write, but you'll be handicapped in life if you don't know how to do it. Moreover, coding itself will largely change as well: programming languages are constantly adopting every higher levels of abstraction and gradually becoming more accessible to a wider audience.