A good king brings order to the realm. God brings order out of chaos at the beginning of creation, and then he hands the project over to Adam to rule in the same way. Not as a tyrant or micro-manager, but offering his strength to bring order to the realm. The reason we depict a king on his throne is to convey order, well-being.
A good king also fights for the security of his kingdom, battling assault from without and sedition from within. That's why he must be a Warrior first. Look at how tireless David is in bringing security to Israel's borders:
In the course of time, David defeated the Philistines and subdued them…David also defeated the Moabites…Moreover, David fought Hadadezer son of Rehob, king of Zobah…when the Arameans of Damascus came to help Hadadezer king of Zobah, David struck down twenty-two thousand of them (2 Samuel 8:1-5).
Think of a Churchill, unyielding to the Nazi's, and the pacifists in his own government that would not hold fast. Or Lincoln, and his unrelenting efforts to preserve the Union. A family with a good father feels protected. Spiritually, emotionally, financially, physically, he is the one to bring peace and covering to his family.
All this in order to bring blessing to his people. "From the fullness of his grace we have all received one blessing after another" (John 1:16). Nehemiah discovers that his people are being fleeced by their own officials, and demands their grain, oil and lands be restored. He refuses even to take the booty allotted to his role. David insists that the plunder from the Amalekites be shared among every man, those who guarded the baggage and those who fought. A good king wants his people to share in the prosperity of the realm. Bad kings build their own off-shore bank accounts.