My Ruby girl rarely covers her poop. She will scratch the top of the litter box, but hasn't figured out how to scratch in the litter so it covers her "deposits".
I'm sure you'll get more replies, as I think it's actually quite common.
If there are ferals making themselves particularly obvious in the backyard, my boy sometimes won't cover his poop. In his case, I figure he's trying to send a message to the other cats.
Two of mine cover and cover and cover and cover...you get the idea. But Lily? She poops and leaves. In fact, she runs as if embarrassed by what she’s done. I always know it’s hers because she never covers it up.
Stevie doesn't cover hers either. She spends a lifetime in there scratching at the sides but hasn't quite grasped that she has to dig the litter. Which is strange because she digs BEFORE she goes but seemingly forgets how to do it after the fact. Gizmo usually comes up to investigate once she's done and covers it for her.
Two of mine cover. The third? He poohs then jumps straight up in the air, out of the box and paws at the ground around the litter box.
I've heard explanations of the cat is asserting dominance or feels secure. In my case I think Link is just bigger then the box. He can't stand in the box and cover without stepping in the deposit. And Link does have the largest cat litter box.