Killer whales live mostly along the foreshore, and sperm whales mostly in the deep ocean. Each is the apex predator of its realm, but who is top overall? The only nonhuman predator ever recorded to kill a sperm whale is the killer whale in pack, though instances are very rare. Likewise, the only nonhuman predator ever recorded to attack killer whales are sperm whales, though these instances are even rarer. These are separate occurrences, with no recorded instances of each attacking the other simultaneously as if at war.
In many ways, their relationship is rather like that of lions and humans on land. When killer whales attack sperm whales it is as its prey and food, when a sperm whale attacks killer whales it is to harass them. An obvious question (if sperm whales do prove sapient) is: why haven’t sperm whales ever made a concerted effort to wipe out a species that presents such a lethal danger to them and their children?
The answer might be for moral reasons. This is seen on land with tigers co-existing with humans in India for at least a thousand years after human population densities made their preservation a more difficult task than their elimination. This however, is not my favoured answer.
An apex predator has a massive impact on the entire ecosystem, and to remove it entirely can invite disaster. So… could sperm whales have reasoned all this? Personally I think a sperm whale civilisation would most likely have discovered this rule the same way we did. The evidence also points to them having learned the hard way.
Many assume that glaciations are a time of lower global productivity. This might be true, yet it is hard to know for sure since lower temperatures boost ocean fertility. The Weichselian glaciation should have been the best of times for an apex predator in the oceans, yet at that very time some unknown force was pushing killer whales to the brink of extinction everywhere except off the coast of southern Africa. The genetics imply that before this its population numbers had been stable for hundreds of thousands of years, and that this same period did not present a genetic bottleneck in any other marine mammal.
Also of note is the unusual behaviour displayed by modern resident killer whales to their transient brethren. Despite having completely different diets with no overlap, residents chase any transients that stray within their reach for miles and savagely rake them with their teeth, as if their very presence in the area presents a danger to them.
If I am reading it correctly this gives a possible timeline for the rise of sperm whale civilisation. Their rise might have began only around 40-50,000 years ago.