There is one case where they are useful - when you don't have enough production slots to build the more efficient units. Some examples are...
you want to build navy in India, and there are only 3 slots. So battleship is an efficient use of a production slot - you could build 1 destroyer and 2 subs for the same cost. While it is a better use of 20ipc (3 hit points,6 attack,4 defense vs 2,4,4 for battleship) you can build more if you have the income.
another reason to purchase a battleship is when your navy is doing trading - ie lots of battles, or multi-wave attacks. if you think of say a 1-2 punch on Japan's Navy (ie US attacks first, and UK second), then provided the first attack by the US doesn't win, the battleship gets its 2hp back for the second fight. So it kind of has "3 hit points" in a multi-wave attack.
As a simplistic example, consider a two wave attack of 3 bombers, then 4 bombers. If we have 64ipc, then 8 destroyers gives maximum hp. This has around a 45% chance of at least 1 destroyer surviving. If you have 3 battleships, which cost 60ipc, this has a 60% chance of at least 1 battleship surviving. However, the efficiency gain tends to be when the first attack is smaller. In the example, if you switch the order of attack, so the 4 bombers go first, then the 3 battleship defence has 45% chance, whereas the 8 destroyer chance stay about the same