I think you have it opposite. Aren't there far more examples of peaceful transitions to liberal democracies (ie, almost every country who had a monarchy in Europe and or were under control of said countries... and now has a parliament/republic).

Albeit it took longer and it was "gradual" but few of them had the hyper-violent post "vanguard" revolutions events that resulted in some of the worst tragedies in history?

https://en.wikipedia.org/wiki/Great_Purge (note famous french liberal Jean-Paul Sartre attempted to cover up news of this event in the west because he thought it would hurt the spread the revolution to the global "politeriat")

https://en.wikipedia.org/wiki/Cultural_Revolution

https://en.wikipedia.org/wiki/Reign_of_Terror

Almost all violent revolutions have resulted in a stain on world history. Yet the (less news worthy) numbers who gradually adopted independent courts and shifted from monarchy to republican/parliamentary power are much higher, and none of them had awful mass murders of people whose ideas weren't "in line" with the revolutionary ideology, not long after the revolutions.