> In this case large bureaucracies are everywhere in the public sector as well, where, at least to first order, price mechanisms, profit maximization etc. are not the driving force.
I'd say that large bureaucracies are endemic to the public sector in large part because they can't use efficient price or profit mechanisms.
A firm doesn't typically operate like a market internally, but instead it operates like a command economy. Orders flow from the top to be implemented at lower levels, feedback goes the other way, and divisions should generally be more collaborative than competitive.
Bureaucracy manages that command economy, and some amount of it is inevitable. However, inevitability does not mean infallibility, and bureaucracies in general are prone to process orientation, empire-building, and status-based backstabbing.
> ranging from the mental health of employees
Nitpick: I think that disregard of employee mental health is bad, but I don't think it's an unpriced externality. Employees are aware of their own mental health and can factor it into their internal compensation/quality-of-life tradeoff, staying in the job only when the salary covers the stress.