The stern walk also indicated that the vessel (usually a battleship) was a flagship and was used by the Admiral and his staff since his night quarters were located in the stern (least amount of vibrations and not subject to waves smashing into it like the bows!).
Also regarding the sternwalk HMS Prince George was rammed (accidentally) by her sister HMS Hannibal when they were in the Channel Fleet, off the coast of Spain, Prince George was holed badly below the waterline and was in serious danger of sinking, when she reached Gibraltar the stern walk was awash! She was patched up and returned to Portsmouth to be repaired properly. Prince George did have a reputation of being an unlucky ship she was involved in no less than three collisions involving a battleship (HMS Hannibal), a German Armoured Cruiser (SMS Friedrich Carl), and another British ship- an armoured cruiser (HMS Shannon). One of the only bits of luck she had were during the Dardanelles campaign when she was torpedoed but it failed to explode!
When I was on HMS Edinburgh the deck area beneath the flight deck was used for the smoking area, but not whilst the helo was in use above for obvious reasons. Sternwalks are not needed now because the pomp and ceremony of visiting VIPs do not require cabins anymore with private walkways and the lack of space on modern vessels do not allow for such frivolous decorative features. They are, after all, warships not luxury cruisers or liners but back in the late 1890s it was all part of the prestige of the fleet.