My personal preference is for as much similarity between my gun's function as possible. I wouldn't want a trigger that I had to push forward.
Then I guess you wouldn't like this trigger:
It's a pre-war Pacific double set trigger. The front trigger is pushed forward to set the rear trigger. It only fires if set, simply pulling the rear trigger won't fire it. Krag converted to single shot, chambered for .22 Maximum Lovell, built by Hervey Lovell circa 1939.
Then there's Martinis, most of which don't possess a safety:
Protocol when hunting is to keep a round up the spout with the breech opened. Snap it shut when wanting to shoot. .357 Maximum, maker unknown.