I increasingly feel that almost every business would benefit from having someone with programming experience on-board. This comes from observing that businesses tend to have a lot of ad-hoc processes and unique requirements, for which there is no software package to buy - not without throwing away huge parts of the processes and rebuilding them in a "standard" way. However, a lot of those unique areas could be improved with a help of someone who's capable of writing small programs and scripts to glue things together.
A random example: my SO often works with high-res photos of their products, and sometimes this involves modifying them to suit the random requirements of other businesses. Something I currently solve for her by running ImageMagick one-liners if she needs more than a few photos modified. A person with basic familiarity of shell scripting and CLI tools could improve their workflow and keep improving it on-demand, as the requirements change.
I agree with your sentiment, but I think most business would already fare very well with having someone structured with project management skills in significant leading position.
Without that, working as a programmer in such disorganized team, you will mostly spend your time working "against" them. It's like you are trying to glue things together and people will just go and and rip those glued together things apart constantly.
I also think you would be surprised at how many businesses both do, and really want and value, software - but don't have anyone convincing to do it for them