@johnlitt They were never "the first to loose their head", they were ont he battlefield, it is true. But usually far off on a hill top somewhere giving orders. This was, in practice, less about having skin in the game and more about them being able to convey orders and negotiate in real time due to the lack fast long distance communication.
They were almost always well protected and kept out of harms way. If they died on the battlefield they were often the last one to go, though there was enough distance between them and the front lines that even then they would likely get away safe and sound.