Let's talk about maps. They help us navigate the physical world. If I want to find my way from Pittsburgh to Cincinnati, a world map will not be of any use. Sure, the map tells me that Cincinnati is generally southwest of me, but I need to know relevant details like highways, bridges, and so forth. But maps can just as easily be too detailed. I could become overwhelmed with topographical information and names of irrelevant farmsteads along my journey. At some extreme, maps become worse guides to the physical world as they become more detailed. This is because a 1:1 mapping would just be an exact replica of the world. I'd need a map for my map. A good mapmaker doesn't just need accurate knowledge of the physical world: a mapmaker also needs to know what his users want to accomplish with that map so that he knows which details to include and which to omit.
Anyone who wants to boil down history into easily digested lessons and rules of action faces the mapmaker's dilemma. Treat history too broadly (like a world map), and you'll only be able to come up with useless bromides. Get too far into the weeds, and the specificity of each historical moment will make any potential lesson inapplicable to other situations and contexts. So in order to write a "useful" history, you'd need to know exactly which details are going to be useful to your reader and exactly which details are going to be needless distractions.
Unfortunately, this is a near impossible task. The problem isn't just that history is more complex than geography. More importantly, the needs of statesmen, generals, and entrepreneurs are less well-defined than the needs of a motorist. The problem is further compounded by the fact that political and economic landscapes shift faster than geographical ones. Taken together, this means that no one can write a definitive study that will unquestionably prepare a world leader for the next crisis.
Nonetheless, I wish that all powerful people had a better grasp of history. Why? The serious study of history can make you a subtler, more nuanced thinker. A cursory study of history will only leave you with pat generalizations that might well lead to disaster if followed schematically. In no way can historical events be reduced to a list of if/then propositions that anyone can follow in order to achieve success and avoid catastrophe.
Perhaps the most useful lesson to be drawn from history is epistemological humility: the longer you study a topic, the more complex and confusing you realize it actually is.
As for Hitler: rummaging through history for anecdotes that support an already chosen plan of action is nothing new. But history is full of narratives and anecdotes to chose from. Hitler's choice tells us more about Hitler than it does about the effects of studying history. Incidentally, maybe Hitler would have been better served by reading about Mithridates instead of the Mongols. Would hitler have been deterred by the story of a leader who indulged in some genocide before ultimately finding himself holed up in his stronghold, surrounded by enemies, and trying to take his own life? Or maybe Hitler would have just been comforted by the line "Mithridates, he died old." Again, that choice would say more about Hitler than it would about the value of history.