In terms of his generalship, you must remember, the US revolution wasn't inevitable, at least not at the time and place it happened. It is quite possible that the continental army could have folded in the early years of the war, and the colonies, in whole or in part, would have accepted a peace overture from Britain. Remember, even a few years before the Declaration of Independence, most people weren't looking for outright independence, and there were many supporters of the crown well into the war.
In terms of government, you forget how new America was. They looked at themselves as an offspring as Europe, but they had no real example in Europe for a Presidential form of government. They talked of ancient Rome, but really they had no examples. After revolting from the British monarch, people were suggesting governments with 3 presidents, governments without an executive, and throwing other ideas out there. Meanwhile, some conservatives were talking about making Washington king, mistrustful of any system that would require changing your head of government every few years. The fact that Washington wanted a republic shot down any thoughts of him being named king; the fact that he would be the first president let people have confidence in creating the office of President with as much power as it did have.
Roosevelt couldn't exist without Washington; there would never have been an office with that much power created if there hadn't been a Washington at the start.
A significant number of democracies today around the world have a Presidential system of government. They're all offspring of the American system designed for Washington; Washington's actions (setting up a cabinet, stepping down after 2 terms to keep it from being a permanent office, etc.) took that theoretical system showed how to make it work in practice. Sure, it's been adapted over time both in the US and overseas, but it's still very recognizeable. In no way was it preordained.
This isn't myth (although Washington had more than his share of myths created about him). Washington isn't great because he was extroardinarily brilliant or that because he had a perfect character. But he was great because he was someone people could believe in, because he always was keenly aware that he was setting an example that generations would look to, and because he turned down more power than he could have taken.
Without Washington the US might have gotten independence, but the government that was eventually formed would have likely been quite different. It's quite possible that no form central government would have ever emerged, and we would have been left with a loose confederation, with individual states forming their own alliances with other countries.