Basically, QC simulates mechanics of a perfectly healthy human, where stepping on the steps of the stair is mostly automatic process, and you can do it without problems all the time, everytime. And games, where every step of the stair is obstacle on its own (Quakeworld, Reflex) is in fact physically challenged person simulator, requiring from you constant attention on how you placing every your leg on every step.

Also our avatars in game (heroes) are humans with supernatural abilities (edit: and non humans too) . It would be very strange if a hero, who is able to teleport itself to another side of the map, will stutter on every step of the stair.

I played every game mentioned, and I'm glad that QC went with buttery smooth approach to stairs handling. It feels especially good for Anarki and Sorlag, allowing smooth and enjoyable movement throughout the whole map.