This is a handwaving assertion. It happens to be strongly correlated with the way our society(ies) allocates labor, but is not something inherent to the labor/wage relationship. It's not hard to imagine a world in which people do things because those things matter to them, or are interesting to them, or both.

Graeber didn't call them "Bullshit Jobs" because the jobs required dealing with bullshit, he called them "Bullshift Jobs" because the actual stated purpose of the job was at best deeply suspect and at worst, well, bullshit.

There is a better fundamental critique of "Bullshit Jobs" which is a little more sophisticated, I think. That critique says that the reason people get confused about the meaning and importance of their job is that our economic system has grown too complex for them to really understand the role they play. The division of labor has reached such extreme levels that it is very difficult for many individuals to grasp how their "apparently meaningless aka bullshit" jobs could be contributing anything at all to the world. But their inability to understand or visualize this does not mean that their work is, in fact, meaningless or without value.

I admit I only skimmed it, but I thought the point was "the employer" is not a homogeneous entity. "The employer" therefore doesn't make the wage decision. Managers with some extreme perverse incentives do.

What's bullshit is the idea that as soon as an enterprise does something inefficient, boom, they'll be outcompeted. They might, eventually, if no market failures or regulatory capture exists. So in reality, large and even small/medium organization with a successful pattern can tolerate a lot of bullshit.