Germans had a lot of trouble designing ships in the 1930s, in part because of the enforced delay due to peace treaties.
In part because they were trying to push the treaty limits to the limits and beyond.
In part because they had limited ocean going experience, running commercial ships through bad weather is not the same. Merchants can slow down, divert, delay.
Machinery was changing constantly, something was changing every few years. Germans skipped a lot of the 20s, this is on top of not staying on top of things in the late teens. Germans had to stay with coal or mixed firing when others were going to oil. Not everything the US and Britain did was oil powered but they were building a lot more oil powered ships than German was in 1916-20. Sometimes you fail but that helps earning.
Germans could copy what others had done but that means you are one-two generations behind. Germans tried to leap-frog everybody else but when you are jumping from an unsteady base using weak legs??
Germans seemed to be a bit split-personality in their tactical thinking/gunnery (they were not the only ones).
In WW I they liked high velocity guns which simplified fire control at medium ranges (ranges in the mid teens of yds/meters), allowed for smaller openings in the faces of the turrets and allowed for good penetration using slightly smaller caliber shells. There were problems with this approach, like greater dispersion and short barrel life.
As far as Destroyers go, just about everybody screwed up the type of guns/mounts they needed. They went for the high velocity low angle guns for surface fire but failed to take into account the problems of firing from a 'lively' small ship compared to large heavy ships. Same gun on a destroyer deck does not have the same
effective range as it does on a battleship deck. They also under estimated the amount of fire control needed (weight/size of directors) and also the amount of ammo needed for more than one short engagement per cruise/mission.
A lot of the the German ships look good on paper but they didn't work well in practice. Unless a lot of the problems were fixed changing from BB/BC to Carriers just means carriers with the same problems. Same for cruisers and Destroyers. Germans were proponents of air power but their naval AA was not really that good. Again the paper specs were good (sometimes) but the actual effect was a bit lacking. The Germans with the destroyers were only a bit behind some other nations (the US was in a class of it's own with the 5in/38 despite not having proximity fuses when coming up with the idea). The German 5in destroyer guns had less elevation than most British 4.7in guns. The German 37mm AA guns were pretty much rubbish.
In a calm sea, in good weather, with ammo close at hand, they might reach 30 rounds per minute per barrel.
The ranges given are an illusion, Tracer burned out at 4800 meters which is about 1/2 the max range and trying to control fire by watching tracer at that distance is futile. Later in the war they increased the HE payload by 4 fold by cutting the tracer back to 1200 meters burn out.
In 1938-40 the idea that a carrier should devote hundreds of tons to a battery of 15cm guns needed a rethink. What were smaller German carriers going to do? with hindsight we can say get rid of the 15cm battery, but given the thinking of the time? Small carrier gets only 12 guns or even just 8 guns?
Germans have an AA problem. The 10.5cm AA gun is a decent gun for AA (?) but it is too light for anti-ship work. 15-16kg shells don't give the effect desired. British 4.5in AA guns fired 25-26kg shells. Not great but in a night attack by enemy destroyers/light cruisers? Germans don't have a lot of choice. The 12.7ch/5in destroyer gun doesn't fire fast enough to make a good AA gun and it needs new mounts/turrets, etc.
The Saratoga and Lex had their 8in batteries but that was in the late 20s. 3 years after completion of the carriers the US only had 5 cruisers with 8in guns (in 1930) in commission.
In the next 10 years with lots of cruisers and modern destroyers the 8in cruiser battery made a lot less sense (they could rely more on escorts) and plans were made to take the 8in guns off and replace them with 5in/38s to beef up the AA battery. This took a while.
Some of these alternative strategies rely on not just changing the types of ships the Germans built, but rely on changing their propulsion technology. Their knowledge of sea keeping,
Their perspective on naval gunnery and their perspective on AA armament and their perspective/perception of ASW. The Big German destroyers carried between 18-30 depth charges most of the time. Not enough for escorting raiding forces in the NA. You can fit more, what do you want to take-off? The reload torpedoes? one of the 5in guns? a few 20mm AA guns?
What do people want the "small" 2000 ton destroyers to carry for armament? surface armament, AA armament, torpedo armament, ASW armament.
The German 12.8cm/5in gun first went to sea in 1932. Maybe you don't need that long but developing guns (ammo) takes time.