What are the Mogami class giving up to have more launchers, less expense, and less crew?
Mogami was specifically designed around minimal crewing from the start, to the point where the ship can apparently operate with as low as 60 people onboard in a worst case scenario. This has been achieved by cutting "redundant" system controls throughout the ship, and basically routing literally everything through the CIC. Examples would be damage control spaces outside the CIC and the engine control room have apparently been eliminated, everything is controlled from the CIC and bridge without local redundancies. Their engine room is designed to be operated without manning at all.
It is very important to realize the purpose that the Mogami class was designed for, as a strictly second line, low cost, low manning replacement for existing Japanese destroyer/destroyer escort classes alongside mine warfare ships from the 1980's/before. They've aggressively cut manning requirements and construction costs (through what is mentioned above/below and items like not fitting VLS) to make sure they can bring ships to the fleet on the cheap, and actually man them.
This doesn't even get into the fact that Japanese ships generally have far less stringent design standards and survivability requirements, largely due to the fact the JMSDF has no real combat experience and desire ease of construction/low cost which comes from these lessened requirements. Even in the warship designs they've heavily taken from US counterparts, they drastically cut requirements to ensure lower costs. Examples would be with the Kongo class (based off the Burke), they have far less comprehensive CBRN facilities, shock requirements are below US basic requirements, they've broken US design/build requirements for unbroken cable lengths internally, with redundancy lost from double stacking cables inside passageways as well. The Japanese also run electrical cables and put other internal components within the double hull itself, alongside generally using much closer to a mercantile standard versus a "warship" construction standard. This is another reason why Japanese surface ships seemingly have shorter careers compared to the international norm.
Even by international standards and especially in comparison to other vessels of their size/tonnage, the Mogami class are frankly death traps. If they take any kind of hit or reasonable bit of damage, the total lack of redundancy and the small crew overall basically dooms the ships immediately. Japan accepted this risk due to their doctrine of domestic use, and the fact they frankly needed ships for low crewing requirements/overall build cost. This is what is missed when people compare them to other designs and try to figure out how they get everything they have.