I'll suggest an alternative approach that might stimulate your neurons. Look back at the ways that your life is improved reading code today compared to twenty years ago. When I look back, the highlights for me are:
a) version control, and
b) automated tests
Forget all their benefits to the people writing code. For me, the guy with one afternoon to make a tweak to an alien codebase, it has been invaluable to have not just the current snapshot of a codebase but a story of its evolution so that I can see what the skeleton of the program used to look like in a simpler time, and gradually play enhancements forward atop it. It has also been invaluable to be in situations where I can go, hmm why do I need _, why don't I just rewrite it as _, try it, and find a failing test with an enlightening name.
What's common to these two ideas is that they are additive. You don't have to give up programming languages. You just need new ways to share information between programmers besides just the code that runs "in production". My current favorite candidate for the next augmentation for codebases is logs. More info: http://akkartik.name/post/tracing-tests. If that whets your appetite feel free to get in touch. My email is in my profile.
 More details of how this helps: http://akkartik.name/post/wart-layers
Programming as it is now is a 2 way communication mechanism, we are writing code for other humans to understand, but for a machine to translate into what we intend for the machine to execute.
So, your point of making code a better human to human communication mechanism is absolutely correct.
What I really wonder about is what set of tools could exist that could solve whole sets of low level problems that we are specifying now that we shouldn't. Sort of like, right now we have blueprints and so on, and then humans look at those and build a house. Yet, with 3-D printed houses, you feed a set of materials and specifications into a machine, and you get a house built for you.
What is the programming equivalent that would allow us to "3-D print" software, so to speak? For physical things, it seems to be the combination of 3-D CAD systems, 3-D printers, and maybe some thought about how things need to be designed to fit this approach.
I have no idea exactly, but I could see a future where instead of paying people to hand craft all the code, that a series of features, modules, structure, etc. are specified, and the software is just "built". There would be more effort in the specification, but less on the build.