Xinhai was far more of a coup in practice. Once the army has abandoned the Qing, their goose is cooked at being anything more than a client.
Asian and by extension Chinese politics are defined by this rule: the strongest force gets the most support. In most cases, it's whoever has the most military backing. It's how the emperors secured the loyalty of the populace, how Chiang Kai-shek got in power, and how Syngman Rhee beat all his other rivals (although he had the US's favor too).
With most of the army having abandoned the Qing, not even foreign intervention from any European power could save them. Not to mention that in Western eyes, the Qing were still embarrassingly backward and decadent.