since this is a DDG thread I was hoping to talk only about warship production
warship production and commercial shipping are two totally different entities
It means these shipyards can produce even more, even a lot more, if they scaled back their commercial ship production. The main bottlenecks would be the supply of machinery components (engines, gearboxes) and components for the sensor and weapons systems which are external and comes from somewhere else. The commercial ship production also indicates that these shipyards have much larger dock capacity than Bath or even Ingalls, as the docks needed for today's commercial shipping are as big or bigger than those used for aircraft carriers as many of these commercial ships are as big or bigger---300 meter to 400 meters, with containerships now increasingly at 400 meters. We have seen from pictures, these docks can easily accommodate building 4 destroyers in one sitting.
The most important part is the skilled labor. When you have a strong commercial base, you also sustain technical colleges that train labor into professional shipbuilders, such as welders, etc,. It develops this ecosystem that breeds and sustains this labor pool. You not only have capacity but you also have a sizable labor resource. On the other hand, a dwindling and disappearing commercial bujild base means this training infracture and ecosystem is eroded, and will continue to erode further, and as these colleges close, you get less and less of this labor pool.
The shipyards can produce destroyers eternally like hamburgers off a fast food if it were not for the PLAN's ability to digest the new ships, training crews, supply of officers, etc,.