Why don't we read of this happening more often? Would his family and servants peer pressure him into staying in his palace until the enemies took his city? What would have happened if, say, a Bronze age Assyrian or Hittite king tried to disguise himself as a servant when the enemies stormed through the city gates? Would the invaders just torture people until someone pointed him out? Has this ever happened?
Was definitely possible but it can of course go wrong if you are recognized (e.g. according to Suetonius Nero was recognized by a retired member of the Praetorian guard when trying to flee Rome on horseback).
Velleius Paterculus has a nice play on the motive of the coward king disguising himself to escape death:
Eodem fere tempore Athenae sub regibus esse desierunt, quarum ultimus rex fuit Codrus, Melanthi filius, vir non praetereundus. Quippe cum Lacedaemonii gravi bello Atticos premerent respondissetque Pythius, quorum dux ab hoste esset occisus, eos futuros superiores, deposita veste regia pastoralem cultum induit, immixtusque castris hostium, de industria rixam ciens, imprudenter interemptus est
Almost at the same time the Athenians ceased to be ruled by kings, the last one of which was Codrus, the son of Melanthus, a man that must not be passed over. For, as the Spartans were pressing the Athenians hard in a great war and because the Delphic Oracle had foretold that those were to be victorious whose leader would be slain by the enemy, he laid aside his regal vest and clothed himself in a shepherd's garb; he then blended into the hostile camp and was unknowingly killed while provoking an argument about diligence.
This isn't even limited to ancient history. Santa Anna tried the same thing in the aftermath of the battle of San Jacinto in the Texas revolution, in 1836.