For drivers, the idea of cyclists rolling through an intersection without fully stopping might sound dangerous—but because of their slower speed and wider field of vision (compared to cars), cyclists are generally able to assess whether there's oncoming traffic and make the right decision. Even law-abiding urban bikers already do this all the time: because of the worry that cars might not see a bike, cyclists habitually scan for oncoming traffic even at intersections where they don't have a stop sign so they can brake at the last second just in case.
There are even a few reasons why the Idaho stop might even make the roads safer than the status quo. In many cities, the low-traffic routes that are safer for bikes are the kinds of roads with many stop signs. Currently, some cyclists avoid these routes and take faster, higher-traffic streets. If the Idaho stop were legalized, it'd get cyclists off these faster streets and funnel the bikes on to safer, slower roads...
If all this sounds far-fetched to you, look at the data. Public health researcher Jason Meggs found that after Idaho started allowing bikers to do this in 1982, injuries resulting from bicycle accidents dropped. When he compared recent census data from Boise to Bakersfield and Sacramento, California—relatively similar-sized cities with comparable percentages of bikers, topographies, precipitation patterns, and street layouts—he found that Boise had 30.5 percent fewer accidents per bike commuter than Sacramento and 150 percent fewer than Bakersfield.
A cop stopped me in the U-District a few years ago after I failed to come to a complete stop at a stop sign. There was no traffic coming in either direction—and I had slowed down (my days of bombing through intersections are over). But the cop explained as he wrote me a ticket that I had to apply my brakes and come to a complete stop, take one foot off a pedal, and put that foot on the ground. That's a legal stop. I replied: That would be like telling a driver he had to put his car in park at a stop sign, take the keys out of the ignition, hold them out the window and jangle them. He handed me the ticket.