Well, just for one of them, Classrooms objectively benefit from incorporating some elements of collaboration in addition to hierarchy. Teaching students to express autonomy and actively participate in learning, rather than being reduced to passive rote-memorization observers with no agency, has consistently been shown to result in better overall outcomes. Disruptive students will, of course, exist; but by and large the vast majority of students respond well to having some degree of control over their own learning.
I certainly think that collaboration is of significant utility in hospitals and development studios, and probably has significant utility in musical theater groups. I don't know enough about engineering firms nor fire departments to speak to those things. Sports teams already have a mix of collaboration and hierarchy.
To turn your question around: do you feel that hierarchy-based leadership models would work in other areas of life that typically employ consensus, such as friendships, marriages, legislative bodies, professional associations (e.g. the AMA), or academic consortia?
Because I can cherry-pick associations of humans that do not have a rigid, top-down hierarchy just as easily as you can cherry-pick associations of humans which do in fact have one. For example, you forgot armies.