In American universities, why are academics placed in managerial and administrative functions?

I'm not sure this is limited to the US as it is a fairly traditional view of what a Faculty should be. Traditionally a group of scholars shared administration as needed. When things were small, not much was needed. Some universities today, though probably mostly small ones, take this idea of Shared Governance very seriously.

In some highly regarded colleges. department heads, and possibly even deans, are elected by the faculty from among their members and likely serve for fixed terms, possibly renewable or not.

Such administration duties usually come with a reduced teaching load.

Some older professors may find that the teaching and research responsibilities are becoming burdensome and want to participate in a different way. Sometimes an especially active researcher with a national or international reputation is imposed upon to take on such duties to add to the "stature" of the institution. It can be questioned, of course, whether that is a good plan. If there is sufficient clerical and professional staff this can work, but as you note it can also break down.

In general, though, such places are willing to accept lower perceived efficiency for hoped increased collegiality.

Some such places, but I don't have wide enough experience to say all, are also more "professor oriented" with rules and regulations more favorable to professors - teaching and advising loads, for example. This can be a good thing (or not). It can also be a good thing for students as it may also mean fewer regulations to have to deal with and a more personal relationship with the faculty. If you apply to a professor, rather than to the institution, you have the beginning, possibly of a long lived relationship.

As suggested in a comment to another answer of mine, I'll expand my sentence "We rarely hire "professional managers in academe, because we do not trust that they know what is going on here."

That is, the goal is not profit, nor maximal efficiency (necessarily), nor any other of the obvious for-profit measures. It becomes dicey at the point where Deans and VP's look tooooo much at "external funding dollars". By the latter measure, all engineering is more important than all literature, music, arts, history, ... And, yes, many administrators apparently act on this criterion.

But we do tend to think that it would be worse if/when "professional managers" truly dictate what happens at universities. The objections are too voluminous to begin to account here. One of the points people would raise is that "improvement of collective understanding" is not necessarily measurable by any accounting practice.

Yes, administrators surely do like simplistic numerical measures... whether or not they capture reality. "Impact factors" are a hilarious current example. Other automated administrator-ready "metrics" are easy to acquire, tho' usually for several tens or hundreds of thousands of dollars... which will not go to faculty salaries or tuition reduction, btw.

Recap: academics do not trust that professional "efficiency experts" or "metrics admins" will have any sense whatsoever about what we're trying to do here.

... and with good reason.

I think one crucial factor is the academic environment. For any outsider the inner mechanics of a university are very hard to grasp. This is a process that takes years. Even experienced faculty that changes institutions expects some "getting acquainted" time.

This in turn is linked with the freedom senior academics enjoy. The boss-employee relationship is limited to the point that it is practically non-existent for senior faculty, while post-docs and grad students are responsible to their PIs. (Again, the exact dynamics are much more diverse and complex, so take this as a simplification).

Therefore, any "managerial" position is strongly rooted in respect and experience more than the executive authority of the role. A leadership position requires the trust of peers that the holder will invest his best effort for the benefit of the institution and that this best effort will be good enough or at least as good as anyone else could be expected to accomplish. Even under those conditions, there are still factional undercurrents in almost any university that struggle to improve their position and can make life for the office holder difficult.

Now imagine a "professional" financial manager being named a department chair. With neither respect nor credibility from the faculty and with limited power to force his way, what can he hope to accomplish? It takes only a few of the tenured faculty to be less than indifferent towards his existence to make his job very very difficult.

Note that there is also the personal aspect, i.e. the ties and connections academics build during their decades of service.

And as for the practical skills, like accounting or HR management, they become trivial when compared to the time spent managing a lab, research, teaching, community service, etc. any faculty member is expected to complete (successfully!) before he can hope to be granted a more senior position. In other words, those skills are learned as a craft, "on the job". While they might be better developed in some graduate of the dedicated curriculum, this graduate would be very hard-pressed to use them to the fullest.