Your conclusion is spot on. Fuzz generators excel at fuzzy tasks.
"Convert the comments in this DOCX file into a markdown table" was an example task that came up with a colleague of mine yesterday. And with that table as a baseline, they wrote a tool to automate the task. It's a perfect example of a tool that isn't fun to write and it isn't a fun problem to solve, but it has an important business function (in the domain of contract negotiation).
I am under the impression that the people you are arguing with see themselves as artisans who meticulously control every bit of minutiae for the good of the business. When a manager does that, it's pessimistically called micromanagement. But when a programmer does that, it's craftsmanship worthy of great praise.