The square is actually a quadrant of squares, separated by busy streets. The original design was probably ideal for accommodating the various streetcar lines, but today it doesn't work very well. Recently there has been talk of consolidating the quadrants to make one square. PPS has also suggested slowing the traffic and narrowing the pedestrian crossings.
This is a picture of the Square in about 1906.
This card and the next one suggest very little traffic and relatively easy access to the Square.
Here you can see the quadrant and the streetcars.
Today, Cleveland's Public Square is a missed opportunity. I feel confident though, that the City of Cleveland will work to transform this square into the vibrant and lively center it should be.