I guess that depends on how large the differences in construction techniques are between the two types. Aren't 052Ds already produced with modular construction techniques? The most significant technology differences between the two types are at the system and sub-system level and therefore upstream of the shipyards themselves, no?
It's good that you mention that, because I think one of the most difficult tasks for for a shipyard in producing complex vessels is integrating the various subsystems into a ship.
Constructing a hull and receiving delivery of various subsystems for a ship are relatively easy compared to actually implementing all those subsystems into the hull during the construction process, then fitting the ship out after launch and getting them to work properly.
And a ship like what 055 is expected to be vs what 052D is, will almost certainly be significantly more complex in regards to subsystem integration.
There is redundancy, and then there is an unnecessary level of redundancy. In my entirely inexpert opinion, having two shipyards each producing two broadly similar types of vessels crosses that line into an unnecessary level of redundancy (whilst incurring inefficiencies).
Potentially. However, I believe having two shipyards that can both construct high end surface combatants of two types is a necessary level of redundancy given the fact that China's overall geopolitical strategic situation is one where its shipyards are quite vulnerable to attack.
That degree of redundancy/flexibility, combined with the fact that spreading construction of 055 across two shipyards provides a greater spread of experience and advanced work to more workers (mostly in relation to very important domain of subsystem integration), I think would make any slight inefficiencies worth the cost.
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edit: also one other major factor I forgot to add, is that having two shipyards also provides a degree of healthy competition and incentives to improve efficiency and avoid each shipyard monopolizing one type of destroyer each.
So really I suppose it's three major reasons for why producing 052D and 055 at two shipyards each makes sense: providing experience for both shipyards, redundancy/flexibility, and competition.