It's an interesting historical thing:
In many armies through the 19th century in Europe where officer positions were reserved for the aristocracy, officers who were promoted up from the ranks, who got battlefield commissions, were uncommon, but it did happen. They had been through what you describe, what the men at the front went through.
And yet, they generally had a harder time being accepted by the men than some privileged aristocrat because they weren't seen as "proper officers". They violated the natural order of things.
Leadership is a strange thing. Frederick the Great was beloved by his men because he gave them victories, but also because he lived simply with the army. But the point was that as the king he didn't have to. Soldiers have never wanted to be led by somebody like themselves.
Now Patton was a strange bird because he appears to have actually bought into his own myth, including the battles he claimed to have fought in previous incarnations during the Roman Empire and the Middle Ages. So he definitely had some screws loose.
But a lot of his persona, the fancy guns, the talk of glory, did serve a practical purpose of leadership. Combined with his undeniable abilities on the battlefield, this did indeed inspire the guys bearing the hardships at the sharp end.
