well, that ship had no shielding on the bridge. the Connie had a triple hull on the bridge module, so ti was well protected.
however, this was not enough, they added an auxillary bridge in the center of the saucer aaround the comupter core whent he refit it. even this was deemed not enough and they added a third emergency bridge in engineering. then we find out there's a forth emergency bridge in the observation room with the old helm wheel!
I think starfeleet wanted the main bridge for scientific and diplomatic uses, if they really were going to war, most captains would use the auxillry bridge in the center of the saucer.