If anything, your anecdote supports my hypothesis that simple programming can unlock large productivity increases.

Your team manager made a career out of incentivising busy-workers, then suddenly one of the workers come along and proves her, her work and her neat floor of busy-workers pointless? Of course she's going to push back. Nobody likes to be made pointless. That doesn't make her any less pointless, and it's for the better of everybody that she stops being pointless.