Washington and the other founders were heavily invested in the "enlightenment" philosophies that had been heavily circulating in intellectual circles at the time, especially the works of folks like John Locke, Voltaire, Jean-Jacque Rousseau, Immanuel Kant, Montesquieu, and many others. These philosophers heavily criticized the absolutists "tyrannical" governments that were common throughout Europe at the time. They idealized systems that were democratic, representative, and egalitarian.

Partly this was because they saw first hand the many problems and traps of traditional aristocratic and monarchical rule. They had seen the excesses up close, they knew the pitfalls and the horrors. Those philosophers as well as the founders understood that even attaining status in the aristocracy or even attaining the role of monarch or supreme ruler was no guarantor of life, liberty, and pursuit of happiness, aside from the morality of denying the same for one's fellow countrymen. No matter how wealthy or powerful an aristocrat could become in a monarchy, such as the British monarchy, the power existed to take all of that away with a writ of attainder.

Additionally, they were familiar with egregious violations of civil rights such as the use of the Star Chamber (that allowed essentially arbitrary application of the law) which had been curtailed in Britain only in the century prior to the revolution with the Habeas Corpus Act of 1640, and they thought it was wise to further hem in the powers of government through the rule of law. They understood that the rich and powerful could be stripped of their wealth and power by those even more powerful, and they understood that once that happened if there were no protections against the abuse of government powers with regard to commoners then there are effectively no protections for anyone. They also understood, from examples such as the Glorious Revolution, that it was possible for those at the very top to also be brought down, so even being monarch is no guarantee of stability or safety.

Ultimately I think the biggest factor was simply that most of the intellectuals at the time heavily favored the idea of representative, democratic governance and the founders were fully bought in to those theories. Their revolution started out as a complaint for equal status to English citizens and aristocracy but the sentiments of equality, liberty, and democracy became rallying cries for the movement as it gained steam. By the time the war was over it would have taken a dramatic change of course to go against those ideals. Granted, there may have been sufficient enthusiasm behind Washington as the perceived "savior of America" for him to have become King, and there is something to the notion that Washington deciding against it was a significant event. However, he just wasn't the sort of person who lusted for power, nor did he seem to relish the idea of just constantly working on running the country. It's telling that he only served 8 years as President as well.