One just doesn't see this. Maybe every once in a while I'll see a tri-geek on one, but it's rare. So when that happens, I usually figure there's a reason. I think the reason is that most folks prefer to mostly ride with their hands on their brakes. Thus drop bars with nice hoods are the choice for 90% of the time because they offer several hand comfortable hand positions with the fingers either on or very close to the brakes. Bullhorns only have one hand position.
I think the most sensible thing might be to get a set of levers that offer you comfortable hood positions and put on a set of clip-on aero bars to add a brakeless rest position. Another possibility is that if you never ride the drops, maybe a bar with a shorter drop or raise the bars up, with or without clip-ons.