That would, I'm guessing, make things worse by both increasing the risk of t-bone collisions, and giving drivers turning from the cross street even less chance to do anything avert a collision.
It's possible that, short of removing and replacing the bridge (which would have its own consequences, since it serves an active rail line in a major city), the only thing that would actually help much is getting stricter about what size of vehicle people are allowed to operate without special training and a special class of license.