Another commenter raised the ransom point for kings. One of the reasons why higher nobility and the king's household was so visible on the battlefields was that they shouldn't get killed by mistake.
As for the common folk, if you look at actual medieval cemeteries that were excavated and studied, the peasants didn't live long either. The age of death can be assessed by looking at the bones, and already the above 50 cohort is somewhat thin, while the above 60 is infrequent.
You underestimate the effects of hunger on mortality. Prior to introduction of potatoes (e.g., ~ 18th century in much of Europe), failed crops would be a common occurrence, happening ~5-6 times during life of a normal rural person. If two of them happened back-to-back, the resulting mortality was already serious, and older people would often be victims. It made sense to use whatever food was left for the younger, stronger generation which was still able to work.
Famine was basically never a concern for the royalty. We have a record of the English king going dinner-less once, but that is not a threat to your life.
BTW If you really want to find a relatively long-lived sector of the society, it would be the high clergy, which had all the upsides of noble life (food, warmth in winter) and almost none of the downsides (most wouldn't fight, murder was less common). This is the only "job" which saw some 70 y.o.s still alive and active, mostly as cardinals.
Medieval European nobility tend not to die in battle. They were captured and ransomed. Richard III died in battle but nobody was gonna ransom him.
Assassination definitely brings down the average. But a fair number of English monarchs managed to die in bed. (I was gonna write British, but no: the Scottish kings practically never died in bed. Unless they were stabbed in their sleep.)
Fair enough related to battle, but that's not the only risk of waging war. A fair few kings caught diseases from their campaigns - which they may not have at home. Overall from some light Wikipedia browsing, it seemed to me that around 1/3 of medieval English kings died from assassination or battlefield wounds & diseases. Note that Richard III is basically the last Medieval king, I'm talking about earlier periods.
