I think the problem is the boss manages, say, 10 people. Someone points out that the work of those 10 people can really be done by one person part-time and now the boss is redundant because no management is really needed anymore.
Start working for the government, though, and every level of management is keen on having as many people beneath them as possible, and there's no real desire at any level to reduce costs; the less efficient your department is the bigger your budget is and the more important you look.
Occasionally a politician will sweep through with an attempt to cut costs (they're the only ones who even pretend to care) -- the bureaucracy will respond by firing the most useful and publicly visible of their employees to ensure that service levels drop thus justifying their case for an increased budget later on.
I went to my boss and offered to add a forgot password link to the site. His response: "But then what would Peggy do?"
If you want something done - your lawn mowed, a meal made, etc - you'll hire someone. But a job for its own sake? What, are you going to hire somebody to move a pile of rocks back and forth across your yard?
A job starts with a need, not vice versa.
Automation doesn't have to be about reducing staffing costs, firing people, or hiring fewer people, it can be about getting more and better output from the humans on your team. Humans are great, and are wasted by reading passwords over the phone.
Peggy provides better, faster feedback than a "forgot password" link does for the vast majority of the population. Not everyone knows their way around a computer; the HN crowd is definitely not representative in this respect. But plenty of people, especially in older generations, know how to use a phone and talk to someone.
Think of Peggy as a UX hack: she makes non-technical employees more efficient by cutting down by 75-80% the amount of time such people would spend trying to reset their password (using the "forgot password link" method). Alternatively, think of her as internal customer service. Either way, she actually does/did provide value to the organization if the organization was large enough that she could spend essentially all of her workday resetting passwords for people.
That's a touch optimistic in my experience. There are definitely those who would love to cut costs and bump profit. But those who are out to pad their budget and status are more than just direct managers.
In my experience, the more common driver of increased efficiency in the private sector, is department A angling in on department B's responsibilities with offers of being able to do them more cheaply/efficiently.
If you're referring to any non-military domestic stuff, "Occasionally" means "Every year from 2000-present". Head on down to town/city hall and pull the budgets for the last 10 years if you don't believe me.