The Southwest Corridor makes the parallel streets discontinuous from Columbus Ave towards Back Bay, the streets from Huntington Avenue to Boylston Street aren't continuous or paralell for the most part, and then the Back Bay grid is opposite to the major direction of traffic along Mass Avenue. Below Columbus Avenue towards City Hospital, diverting cars onto side streets would make the intersections worse. Worchester St. and Square is a quiet narrow, so that would be a bad idea to put traffic there. Northhampton, Southhampton, Lenox, etc. streets aren't wide or safe for that matter either.
Ralph Adams Cram's Dartmouth Street bridge (can we get the island while we're at it?) would have cut half the traffic off the Harvard bridge and Mass Avenue if it had been built. If the Southwest Corridor Park and other developments didn't truncate the side streets of the South End to Huntington Avenue, it would have diverted more traffic as well in a natural fashion. Through traffic needs to be kept off Mass Avenue through dilution in the first place, not diverted off an already clogged street.