The ship designer in HOI4 generally gives you simplistic trade-offs like more firepower=less speed=more production cost. IRL, the biggest guns were not always the most effective. The Royal Navy decided against 16in guns for its interwar battleships because they considered them to have less damage output potential than smaller guns. While one hit from a larger gun may pierce through the thickest armour, smaller guns fire faster and are more likely to score hits.
All thoughts below based on my reading and I'm only as good as my sources, and in the spirit of a friendly discussion on warships
The RN only commissioned two new battleships in the interwar period, and they both had 16in guns as their main armament
I'm quite sure you're well aware of this, though, and are referring to the KGVs (designed and construction started in the interwar)
Based on Raven and Roberts'
British Battleships of World War Two, the British decided in about Sep 1935 to go with three triple 15in turrets, acknowledging they provided less gunpowder than three triple 16in turrets, but that the treaty limitations on battleship weight meant a 16in-gunned ship would be under-protected. Then the naval treaties came along, and in the preliminary negotiations, the British decided to offer a 14in main calibre limit - while the escalator clause was built into the treaty, it was necessary to order the guns and start work on designing the mountings immediately. Because delay was not acceptable, the KGVs were built with 14in main armament, but their successors, the Lions, were designed with three triple 16in turrets as their main armament (which, on 40,000 tons allowed for a more balanced design, at least in the mind of British designers*).
It's also worth bearing in mind that the 14in Mk VII in the KGVs didn't have a particularly fast rate of fire for a capital ship gun, of about 2 rounds per minute (similar to the Queen Elizabeths, or the US 16in-gunned BBs).
That said, the broader point you make about not necessarily going with the bigger gun, and that rate of fire mattered, very much was a point of discussion in comparisons between 8in and 6in-gunned cruiser designs of the period.
* Which, for what it's worth, I agree with, but my cred here is marginal at best!
The Graf Spee, for example, was defeated by warships that she outgunned. Among other things, her desalination plant had been hit, which meant the surviving crew would run out of drinking water. Lots of small guns probably beat a handful of big guns in most cases!
Graf Spee is a tricky one, as her fighting ability in the short-term really wasn't impaired by the battle at all (whereas Exeter was in a much rougher shape after the engagement) - the loss of the desalination plant was the critical matter, but had the Battle of the River Plate been fought in the North Sea and Graf Spree withdrew to Wilhelmshaven, then it would have been a far less flattering result for the RN. A better example might be the first naval battle of Guadalcanal, when the 8in and smaller-gunned cruisers mauled Hiei at close range?
The whole armour vs. piercing thing is also problematic. A lot of things can go wrong on a ship without its hull being pierced. Smaller shells can still cause an explosion on the bridge or in other vital control areas and put a ship completely out of action. Not every ship went down like the Hood -- many were scuttled because of small shells hitting vital bits that weren't protected by armour.
Bear in mind that critical hits are still possible even if the armour isn't pierced - it's just that piercing the armour makes it more likely that criticals happen. While I haven't crunched the numbers, the general approach in-game seems fairly sound. The most important parts of the ship were protected by armour for a reason, so being able to pierce armour leading to a greater chance of criticals feels to me like it makes sense (although I could be wrong).
Most (all?) major warships of WW2 had alternative control and conning positions, so while a bridge hit would cause issues, it wouldn't stop the crew being able to fight the ship (unless for whatever reason the alternative control/conning positions weren't crewed, but my understanding is that was standard practice for action stations). From memory (and I can look this up - but I'm going from memory, so there's a chance I'm wrong) British, US or both (I can't remember which off the top of my head) could in an emergency control the ship from inside one of their turrets, if both "outside-armour" positions were disabled. Other than the rudder (as Bismarck found out), most critical systems had at least some armour, and often quite a bit.
However, by taking out the director control towers, radar and so on, it was definitely possible to substantially diminish the fighting capacity of a warship of the era, even if it wasn't possible (unless the rudder/steering gear was hit) disable it entirely.
