While true for England, things went a little differently in France with the French Revolution. I'm not sure if it started as you say, but it ended not much differently than a violent overthrow of the ruling class in other countries.
To be clear, the French Revolution is exactly in line with the example, and part of the definition of it; bloody revolutions are often how the middle class takes power to enact democracy.
Note, though, that the means by which overthrow occurs is mostly orthogonal to its consequences; the important thing is instead who's doing the overthrowing. Most coups are done by a small group, who become a new aristocracy after the coup succeeds. Democratization occurs when, instead, 1. the overthrow is populist in nature, but 2. no power vacuum is created for new aristocrats to step into, as the populace (esp. the borgeoisie) have managed to install a new governmental structure that doesn't require dynasty-driven statesmanship and foreign diplomacy policy.
