Yet in reality it has as many layers as other governments and businesses of a similar size.

"Administration" in https://www.britannica.com/topic/Holy-See gives a rough overview.

There's layered mangement for multiple domains of interest.

I think it's also possible that says a lot more about the shoddy metaphors of most business schools than the actual level of hierarchy in the Catholic church (beyond the other discussion we were having about how atypical the CC is as an organization).