There is/was a discipline known as "psychohistory." It is so speculative, and its founding voices (e.g. Erik Erikson, Lloyd deMause, and even Sigmund Freud himself in his later works like Moses and Monotheism) took it to such bizarre and self-absorbed ends, that most historians, if they are even aware of it, find it to be a ridiculous and potentially even to be a form of pseudohistory. Presumably there are some practitioners who are not cranks, though the field's history is so muddy that I would suspect many people who did have an interest in applying psychology to history would not call themselves practitioners of psychohistory, just historians with an eye towards psychology.

But anyway, it exists, but it is not mainstream. One might ask: why not? In part because psychology itself is a rapidly-shifting, maybe-a-science maybe-not field (the diagnostic categories are not fixed over time, and neither are the basic concepts). In part because doing psychological diagnoses of the dead, on the basis of what few scraps of information were preserved in the historical record, is considered quite a stretch even for psychologists (who generally do not endorse "remote" diagnosis of people). And in part, perhaps, because of the association with the rather ridiculous, overly-Freudian approaches that were championed by those who tried to found the discipline.

Psychohistory has been applied to notable individuals, particularly military or national leaders, but also to societies. This idea was applied particularly to the study of Japanese and German militarism-- you can think of works like Ruth Benedict's The Chrysanthemum and the Sword or the many works examining the social psychology of Nazi atavism, I would think first of Gustave Gilbert's interviews with Nazi prisoners at Nuremberg.

Another example would be Norman Itzkowitz' biography of Ataturk. Itzkowitz (a former professor of mine) had a training in psychoanalysis, and his work The Immortal Atatürk:A Psychobiography is a good example of someone with a professional training in both psychiatry and history can do: I’d call it “somewhat successful”

Psychohistory tends to have a dubious reputation because most often the author is inexpert at one or both of the disciplines; so Ruth Benedict was a trained anthropologist, but she didn't speak Japanese or know a lot about Japan before she was tasked with explaining "what makes them so violent". It's often found in intelligence services' evaluations of foreign leaders, so for example the US commissioned psychiatrists to evaluate the personalities of Hitler and Stalin . . . the results aren't particularly impressive.

Psychological explanations often serve as a bit of hand-waving for unprovable assertions: for many years it was claimed that Charles V of Spain gave up his crown and retired to the monastery at Yuste because he was "depressed". When physicians and chemists examined his skeleton, it was found that, matching historical accounts, he was crippled with gout. Wasn't his mental state that lead him to retire-- he was just too much in pain and too crippled.