I think his lack of screentime makes him cool. It is one of those times, I think, that people don't really notice the difference between narrative presence and physical presence.
Catnap is a character that has a lot of both. Physical presence is actual presence on screen. It is when a character is seen doing things. Narrative presence is the presence if a character off-screen, which usually means that we get to see the results of the character's actions on the story.
His physical presence is usually that of a stalking predator. The few times we see him, he is always present for a fraction of time, before quickly disappearing. We hear him walking around, and watch us at the corner of our eyes. But he also has a lot of narrative presence. Afterall, he was the one that lead to Miss Delight becoming insane (in a way). He sacrificed the other Critters to the smaller ones and killed numerous for the Prototype. His actions are really important.
The Prototype is also a character with almost no physical presence, but tons of narrative presence. Afterall, the story of the game wouldn't even be the same without him (no successful experiments, no hour of joy, no Catnap, etc)