Water vapor around the LCL starts condensing and turning from a gas into liquid cloud droplets. This process happens considerably faster once it begins for a variety of reasons, so once you can have cloud droplets, you get a ton of cloud droplets - not a gradual transition from water vapor to cloud. It's almost like a light switch.
Most air masses are relatively homogenous anyways, so unless there are underlying processes causing things like undulatus asperatus, it will certainly appear very, very flat over a large area.
Same reason a loaf of bread is. Clouds rest on the "surface" of the higher-density air below them, and flatten on the bottom because of their own weight.
