Having everyone knowing how to code is the opposite of specialisation. It's inefficient and pointless. If a certain profession needs a piece of software, it's much more efficient for specialist developers to consult with domain experts, write that software, and sell it into the industry. Having every (for example) doctor being able to code adds negligible value, and I would argue the opportunity cost is awful. If my doctor has a choice to become a very mediocre coder or a better doctor, I would hope they choose the latter.
As for the comparison to literacy, there's simply no comparison. Illiterate societies are unable to progress past agrarian economies because illiteracy precludes specialisation, prevents the dissemination of knowledge, and makes it almost impossible to learn new things except by imitation or direct instruction. Literacy is a necessary skill in order to do much beyond dirt farming. Illiterate people can't, for example, even follow a moderately complex checklist. In contrast, I see no negative impact on society if most people can't code.
I don't spend my time studying anatomy; my micro-surgeon shouldn't spend his time studying coding, and I don't see how it would do anything but make him less effective if he did.
A society of part-time coders would do nothing but produce a lot of badly-written toy programs. What's the point?