I think the diagonals were structural. If you look at a cross section of the bridge, the walkway was the bottom flange of the I beam, and the canopy was the top flange of the I beam. The diagonals were the web of the I beam. The cables to be added later were supposed to be stiffeners to help control the bounce of the bridge.
What's questionable is that the diagonals were not steel. They were tensioned concrete. This is kind of unique to this bridge. Everyone knows that non-tensioned concrete is weak across a span. If the tensioning rods/cables in one of those diagonals were loose, that means there was not-enough-to-no-tension in that piece of structural concrete.
As many others have said..... why was traffic allowed under it until it was done? A rush to complete it.