Very interesting question and one that sheds light on how our contemporary thinking is so deviant from the "old ways". To add to what has already been said I'd like to provide some historical background as well.
In ancient times and up until the invention of modern warfare kings/generals/etc. would ride out to battle and lead their armies at the head, often dying in battle, but it was their vocation and their calling to lead.
The song "Saul has killed his thousand, and David his ten thousand." lead foreign kings to think that David was already king when he was still in subjection to the annointing of Saul.
(1 Samuel 18:6 and on into 1 Samuel 21:10)
To see the original meaning of priesthood it's interesting to follow the etymology of "clergy":
clergy
c.1200, clergie "office or dignity of a clergyman," from two O.Fr. words: 1. clergie "clerics, learned men," from M.L. clericatus, from L. clericus (see clerk); 2. clergie "learning," from clerc, also from L. clericus. Clergyman is 1577; clergywoman is 1673. Cleric (1621) was borrowed directly from L. clericus after clerk took its modern meaning. Clerical (1592) was originally "of the clergy;" meaning "of clerks" first attested 1798.
clerk
O.E. clerc, from L.L. clericus "a priest," from Gk. klerikos (adj.) in church jargon "of the clergy," derived from kleros "lot, inheritance" (orig. "a shard used in casting lots"), used by early Gk. Christians for matters relating to ministry based on Deut. xviii:2 reference to Levites as temple assistants: "Therefore shall they have no inheritance among their brethren: the Lord is their inheritance," transl. of Heb. nahalah "inheritance, lot." If the word choice was meant to remind clerics of anything, however, the reminder was lost with the knowledge of ancient Gk. Modern bureaucratic usage is from c.1500, a reminder of the dark ages when clergy alone could read and write.
In ancient thought a king was beholden to his people under God, if the kingdom suffered the king was held personally responsible. The kings owned nothing, not even their body, it was all for the people. The ancient priesthood was held in the same regard, taking personal responsiblity for maintaining the socio-religious order, if they messed up they were held personally responsible. Again they owned nothing, not even their body, it was all for the people under God.
When Nadab and Abihu offered strange fire they were consumed, when Saul disobeyed God he was driven by an vexing spirit until he committed suicide in a loosing battle against the Philistines.
Neither kingship or a priestly calling are reasons for pride, they are deeply humble professions that require a person to give everything of themselves. If a king becomes their nation, as it was thought in ancient times, then there is no room left for the self. If a priest becomes the socio-religious order, then there is no room left for the self. The decadence of past ages is due to king's who thought more of themselves than their kingdom or priests who sought self gratification and pleasure rather than a Godly order.
Isaiah 14:12-15 -
How you are fallen from heaven, O Day Star, son of the morning! How you are cut down to the ground, you who weakened the nations! For you have said in your heart: ‘ I will ascend into heaven, I will exalt my throne above the stars of God; I will also sit on the mount of the congregation on the farthest sides of the north; I will ascend above the heights of the clouds, I will be like the Most High.’ Yet you shall be brought down to Sheol, To the lowest depths of the Pit.