So, for this analogy to be fair, we'd need to have computers which you can't operate unless you know how to use transistors to build logic gates, how to build your CPU out of those, how this CPU executes instructions and so on. Of course, that's "vs just keyboard and mouse".
Of course there's room for improvement, but current computers are not orders of magnitude harder to use than cars. I'd say that they never were, but right now they're not for sure: 3 years old kid won't drive a car, but he can have some meaningful and fun time with a tablet.
Learning programming is secondary issue in my opinion. A "new literacy" is something else: it's ability to stop and think about how the pieces fall together, how they work, how you can make them do what you want. Programming is certainly a way of learning this ability, but it's also full of pointless ritual and irrelevant things and operates on completely wrong - for the normal user - level of abstraction. I don't know what is the most efficient way of teaching this to people, but I strongly believe that we need to teach them this. If we have no better way, then let it even be via programming, it's still better than nothing.
Computers ARE orders of magnitude harder to use than cars. A car has (at the simplified level) a single wheel that goes either left or right and 3 pedals. The hardest concept relating to hardware is what a gear is and why you need to shift it (among a few others).
It is correct though that software CAN be more simple than that in their use. Those pieces of software tend not to solve complex or any problems in our real world though.
When it comes to 'coding as literacy' this has not much to do with using a highly simplified UI. It has to do with the fact that if I want to use most of the features of the machine we call PC, you HAVE to be able to program.
Sticking with the car analogy my kid can have great fun if I show her how to use the horn in the car. It will not allow her to do anything meaningful with the car (getting from A to B). All she can do is use the car as a toy.
I agree with you on the core problem though. Things are abstraced away from everyone in our daily lives in such a way, that people sometimes are unable to be 'precise'. By that i mean the ability to fully describe a problem and formulate an executable solution. I personally don't think programming is the solution to that. Personally I learned that concept in school in philosophy class.