I will often buy 1 or 2 battleships as Japan at some point in the middlegame – carriers are always better if you have free planes available to land on them, but sometimes most of my airforce is busy deep inland, e.g., taking India, or Yunnan, or Siberia. Because Japan is often the victim of a one-two punch by US + UK or US + ANZAC, it’s important to develop a fleet that has defensive staying power, and BBs can help with that.
A typical carrier group might be something like CV, fighter, tac bomber, DD, SS – total cost is 51 IPCs, you get 6 HP and 12 pips of defensive power.
For similar money, you can buy BB, BB, DD, SS – total cost is 54 IPCs, you get 6 HPs and 11 pips of defensive power.
As you can see, the stats are less favorable for the battleship group, but the battleship group holds up much better against one-two punches. If the carrier group takes 3 hits, then you have to either lose an expensive plane, or take a hit on the carrier and land both of your planes, assuming you even have a friendly island handy on which to land them. After taking 3 hits with the carrier group, all you have left is probably CV + fighter – which only has 6 pips of defense and can then be eaten alive by the Australians or the British. You’ve lost a total of 25 IPCs worth of material in those 3 hits (SS + DD + tac).
On the other hand, after the battleship group takes 3 hits, you have damagedBB, damagedBB, DD, with a total of 10 pips of defense, meaning that it might be too risky for UK or ANZAC to do their follow-up attack. Plus, you’ve only lost a cheap sub to the initial attack, for a total loss of 6 IPCs.
So in the particular case where I plan to be in range of one-two punches and a large part of my air force is busy in Asia, I think buying a couple of BBs can make sense for Japan, although even then, I would still buy more CVs than BBs over the course of the whole game.
The only reason to buy a cruiser is if you’re constrained by both a minor factory and your budget. E.g., Australia might buy a cruiser and 2 infantry for Queensland; the cruiser isn’t even slightly efficient, but maybe you need a warship right now and that’s the best you can do with your money.
For what it’s worth, I also miss the old bombardment rules, but we’re already playing with ludicrously easy amphibious invasions. In real life, getting soldiers off of a boat and onto a contested island or beach was incredibly hard and created a huge advantage for the defender. DK solves this neatly by giving the defender free notional hit points that help defend against amphibious assaults – like a bunker that has 2 or 3 HP and rolls nothing on defense. If your group has a high tolerance for house rules, you could try introducing DK’s imaginary bunkers and also re-introducing the pre-emptive bombardment, and capping the bombardment by the number of ground units that actually unload, e.g., if you have 1 infantry unloading with support from 7 battleships, you still only get 1 pre-emptive shot. This is maybe not the highest-priority thing to fix about A&A, though.