Even someone who does "the whole job" is still generally a cog in the machine, as few jobs are in themselves extremely important in the global scheme of things. Indeed t here have been plenty of forgettable prime ministers and presidents. The question is just how much diversity of tasks it takes to feel engaged, and how much scope of responsibility it takes to feel like what you're doing matters.

The exception would be someone like a subsistence farmer. But hell I'd rather work in a factory.