Except experience with the "risk compensation effect" has been mixed. It turns out that sometimes taking away street markings and traffic control devices makes a place safer; in other cases it makes it more dangerous. Specifics matter, that's why it's called "traffic engineering".
If you look at places put forward as examples of "shared space" traffic design they look distinctly Old World -- they're in neighborhoods that are designed around pedestrian traffic. American Sun Belt cities aren't designed around the needs of people, they're organized to maximize the flow of cars. San Diego might well be the most pedestrian hostile urban environment in the world. It has residential neighborhoods without a single store or even playground within convenient walking distance of most of its residents. You need a car for everything, and everyone needs a car. Traffic everywhere is heavy and fast.
Here's one of the San Diego intersections in question, 4th and Broadway. Compare it to a Dutch shared space. Click a few times to move around both neighborhoods to see the difference. Yes, the Dutch city has a lot more bikes, but that's a result of the real difference, which is that the Dutch neighborhood is a destination; most of the people there are going places that are there. The San Diego intersection is a crossroads; almost everyone there is heading somewhere else.
Now you can put a fountain in the middle of the 4th and Broadway intersection; remove all the traffic signals and markings in the neighborhood and put up a four way stop sign, obliterate the distinction between sidewalk and roadway in the area. All these things would probably make this particular intersection safer. But it won't make the city as a whole safer because it doesn't address the underlying planning problem: San Diegans have to drive everywhere. The fast, heavy traffic will simply shift over a street or two on the grid. You'd have to make those same changes on all the possible alternate routes as well. This would make the city safer, at the expense of trapping many residents in commercially lifeless residential neighborhoods.
You can't make the city safer transforming a single intersection or even a handful of intersections into "shared spaces". To make that work you'd have to radically redesign the entire city to eliminate most of the driving people have to do. That's actually a really good idea, but good luck convincing San Diegans to pay to have their city transformed into Leeuwarden. In the meantime people will continue to be killed at the crossroads.