I think both cruiser and battleship retain purpose. For battleships, you absorb two hits, just as a cruiser and destroyer would. But if only one hit occurs against you, you are able to keep your battleship in tact without losing a ship. A cruiser or destroyer would needed to be sacrificed if one takes a hit in battle. Battleships bombard at 4 as well and I believe their is a psychological advantage/disadvantage(depends on if its yours or not)  when you see a battleship. There are also many advantages to having a cruiser and destroyer. Variety is one. They both have abilities such as detecting subs and bombardment shots. Although the cruiser only bombards at 3, it can still be used as an effective weapon. Possibility of hitting twice in one turn instead of once. And also mobility choices. You can keep your ships together or break them apart to do various missions on the board. It allows you to be flexible and with your naval units. I think you have to look at your country and situation, which should be the deciding to whether go with a battleship or a destroyer and cruiser.

The problem I see in this whole strategy is that USA does not need to focus on building a vast navy that is comparable to Japan. They need to concentrate on Europe (hint hint: that was how history played out; Europe falling first then Asia.) USA is much more effective if they concentrate a majority of their forces on Germany and Italy. That is where the game is won and lost.