A Destroyer and a Cruiser costs 20. A Battleship costs 20.
If you buy a Destroyer and a Cruiser together and keep them in the same SZ at all times, I feel it is a better investment than the BB.
Battleship has a 67% chance to score a single hit in a given round.
A Destroyer+Cruiser combo has ~70% chance for either to score a hit, and ~13% chance for both to hit.
Advantage Destroyer+Cruiser
Battleship can take 2 hits before sinking. If it takes only one hit it can be restored to full at no cost
A Destroyer+Cruiser also takes 2 hits, but if the combo takes one, it costs a minimum of 8 IPC to restore to its combined power
Advantage Battleship (slight)
Battleship doesn’t prevent Sub surprise strikes
A Destroyer+Cruiser does
Advantage Destroyer+Cruiser
Battleship has a 67% chance to score a Naval bombardment hit.
A Destroyer+Cruiser combo has 50% chance for a Naval bombardment hit.
Advantage Battleship
By the time WWII was in full swing, the Battleship was mostly a source of national prestige, as opposed to strategic necessity. When the Hood went down, British pride suffered.
Maybe give each Nation a National Objective that during war if there is a Battleship on the map for your nation, it grants you 2 IPC per turn for national prestige.
That wouldn’t make me buy one after the start of the game, but it gives it some more value and adds a wrinkle.