I think the Texas Transportation Institute (non-partisan, not insurance company funded) had a study out a few years ago that had the number of accidents and deaths in shopping centers "very low" due to the typical speeds of the vehicle and the number of conflicting points that required almost constant driver attention. When combined, the driver was alert and looking out for pedestrians at almost every segment of the inner mall route (not the outer fringes of a parking lot) and traveling at very low speeds - typically less than 20 MPH.
That situation can work in some instances. For instance, imagine converting 4th Street in downtown Cincinnati into a mixed traffic thoroughfare. Two-way traffic could be restored, the sidewalks eliminated, and the path become essentially one. The driving lanes - say, one going eastbound and two westbound, could be delineated by paint markings, and on the edges, large landscaped plots for trees and flora. There would be multiple openings, and pedestrians would essentially be able to cross at will and not just at crosswalks. To ensure that speeds would be slow - since it would be the only type of its kind on the city, there could be speed humps, narrow traffic lanes and other traffic calming measures.
Losing the visibility of a curb line and a fixed definition of an automobile right-of-way could work. The 9th Street Plaza, after it was converted from a pedestrian plaza into an automobile route (with few modifications to the pedestrian plaza) was a similar attempt. Cars literally weaved in between large above-ground tree planters, benches, a water fountain and parked cars. It deteriorated fast, though, because the sidewalk was so thin and cracked under just a few years worth of use, and has been replaced by a new auto plaza.