Running the world like a business

Sound of Music
How do you organize people to get something done? Let’s say it’s a hierarchy. What could that look like?
I’ve noticed that lots of people use “business” as their primary model for organizational structure. For some, it’s the only model they seem to need. Over the years, I’ve met plenty of folks who want to run a school or a church or a library like a business. But what are the similarities between organizations and what are the differences? What works in what context? (Remember in the Sound of Music when Capt. von Trapp tried to run the household as if it were the Navy? Clearly the wrong organizational model.)
This is not really a partisan question, though the incoming administration will certainly test some of these ideas. The model is everywhere, and I ponder such things–especially when people seem to equate democracy with capitalism; hiring a minister to hiring a CEO; comparing a school’s success to turning a profit.