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.