Ships of the Wall and battleships
I trust it is apparent from above why BBs are not expected to survive close combat with an SD. They simply cannot carry the sidewalls, armor, internal subdivision, etc., to stand up to an SD's energy batteries in a one-to-one duel, or even in equal tonnages. This is why the Peep BBs are missile heavy, even though missiles are less effective than beams against a hostile SD. Missiles are quite heavy enough to deal with BCs and below (which is what BBs are really intended to fight), and in a stand-off engagement with standard (i.e., pre-pod) missile armaments, a BB has a much better chance of surviving combat with an SD. The chance is still slight in any one-for-one engagement, but equal masses of BBs can throw a larger number of missiles and, hopefully, stay out of the energy envelope. The reason Thomas Theisman took such losses at the Battle of Seabring was that he couldn't stay outside the energy envelope and because he took a pounding from the Manty missile pods on his way in to his own engagement range. The enormous difference between the offensive and defensive mix of a proper ship of the wall and a BB is also why Honor's SDs were able to shoot up the BBs of Operation Dagger in Yeltsin. (And if the Peep force hadn't split up, she would almost certainly have taken out all of Theisman's BBs in the initial exchange, as well, and probably without suffering much--if any--heavier losses than she actually took.)
What a BB is (or was, pre-war) is the most effective system security platform available. A BB is cheaper to build. The same tonnage will go twice as far in terms of hulls. It cannot effectively fight a DN or an SD (although in cases of dire emergency it can try to do so), but it is sudden death on anything smaller than itself. And while it cannot match the acceleration of a BC or a CA, it can (assuming equal compensator efficiency) generally stay between a raider and the critical areas of a system and compel the raider to come to it. This is why the prewar Peeps--who had lots of systems to defend against potential raids (not to mention other internal security concerns)--built BBs in relatively large numbers while the prewar RMN, which had few systems to defend and needed all the offensive firepower it could get, built only DNs and SDs for units above the BC.