Pedestrians aren't required to stop at stop signs, yet can run through them much faster than most bicyclists would. On top of that they can be wearing headphones and much less able to avoid a collission. No one is talking about outlawing pedestrians from treating stop signs as yield signs. One of the reasons is that they give cyclists a head start through red lights, with special zones ahead of motor traffic, and special bicycle-only green lights. It can be much more dangerous to stop at a red light than to run it during a safe period before all the conflicts begin.
Cyclists are the ones who have the most to lose when running a stop sign or light.
Let them decide when to do it. The way many take stop signs today is very dangerous, with so many swinging around corners for those lightning fast right turns without sufficiently looking, e.g. rush-hour violators who sometimes don't even slow for stop signs when crossing bike routes. Cars are very deadly, and cause tremendous public expense. The main opposing argument that I have agreed with is that some cyclists will run stop signs carelessly. I'm much more concerned about the motorists being careless, which happens more often in my experience.