But, then I think of animals. Do animals masturbate a lot? They seem more driven to produce offspring of their own, while competing against rival males. They even kill the offspring of other males.

Then there are the cases where fetuses and babies are intentionally killed, so the male can get back to fucking! This is quite obvious if you have ever raised birds.

I would say that despite the result of procreation, fucking is done for pleasure and establishing dominance and relationships.
As for the killing, I think there is a tendency to kill anything that is not recognized as being one's own family

It would be interesting to see surveys in which people were asked "Do you want to have children?" and compare the results of male respondents vs female.