One of the many problems with Public Square is its obvious disconnect to the city. The square has little vehicular traffic traversing through, a mere 17% of all traffic that approaches the space proceeds through. Furthering this disconnect is that of the pedestrian traffic. Although roughly 20,000 pass through the square on foot, few stick around. During the middle of the day one would be hard pressed to find more than a few wonderers.
One precedent studied to give insight into the issues concerning Public Square is Steel Cloud. Done by Asymptote for the Gateway Competition in 1989, this project sought to address many of the same issues [it is important to notes this project was never realized]. Los Angeles like Cleveland maintains a disconnect between spaces. In the case of L.A. the freeway causes a fissure separating abutting sides. The solution here was a very aggressive monumental structure linking both sides once again, while simultaneously engaging all traffic, pedestrian and vehicular.
This strategy applied to Cleveland would seek to encourage vehicular traffic through the square and would provide various program to attract pedestrian usage.