I've had several cats throughout my lifetime and I've never had one that covered up vomit or hairballs. Now when it comes to covering up what they've left in the litter box, one of my cats doesn't even do that. When I'm cleaning the litter box I always know when he has gone to the bathroom because it will be sitting right on top in plain view. A different cat that I have will keep covering for the longest time, even after it's buried in cat litter. Sometimes I'll say his name and then tell him that he's done a good job, just so he will stop covering. He really works at it too, because cat litter will be flying out of the box. When this same cat vomits, it scares him. He will first howl, then vomit and then run away from it. Cats are so funny and they all have such different personalities and quirks.
Yes, I've stepped on a hairball first thing in the morning too and it's not a good feeling, especially when I'm not fully awake yet and haven't even had my coffee.