When did government leaders like kings and Presidents stop leading troops on the actual battlefield?
what kind of government can a king run ?
The need for Heads of State/Government to be physically present at battles as leaders declined as States became larger, more sophisticated and more complex. Once it got the point where it was more important for a ruler to be an able governor and diplomat than general and fighter, many rulers stopped endangering themselves (and often their country) by being physically present on the battlefield. Also, countries and armies became so large and far-flung it was not possible for a ruler to govern effectively AND lead their forces into battle.
I cannot give an exact date as to the last time, but I believe it to be in the mid- to late-19th Century. The last British King to lead an army in a battle was King George II in 1743, but Napoleon Bonaparte at the beginning of the 19th Century led his armies to battle. Whether he was the last I cannot say. All the information above is relevant to Europe only.