The specific question arose from my historical interest in the evolutionary maintenance of sexual reproduction. The paradox is the fact that most animal and plant species keep reproducing sexually although an asexual competitor should gain an immediate, twofold reproductive advantage. Since having discovered the sociobiological roots of that issue (see here and here), I've been wondering why none of the pioneers, and Hamilton in particular, tried to find a sociobiological solution for it? Thereby I mean a solution that is based on interactions between females and males or female and male gametes.
Not having found an answer in Hamilton's autobiographical essays, I hoped to find one in Segerstrale's biography, therefore jumped straight to chapter 15 (The Parasite Paradigm) and was disappointed to find no answer therein either. As it turned out, however, the answer or hints towards it are scattered across the rest of the book.
Segerstrale is good at exposing the personal streaks (idiosyncrasies) of Hamilton, and one of them seems to answer the question.
This streak was his being not just a normal pioneer, but an extreme one keen on getting away from pastures as soon as the vanguard had arrived behind him. At the same time he was a 'nurturing mother' to his fledged hypotheses, for example, he re-derived Price's equation and sorted out the issue of group vs. kin selection (he saw both as special cases and inclusive fitness as the general theory). But he nevertheless craved for something different. Hence he was not willing to assimilate this new issue to his old theory, though he did invest 'parental care' into his eldest brain child. Just one quote to give you a hunch of the scattered passages that hint towards this answer.
With the Fox volume chapter [Hamilton 1975, 'Innate social aptitudes of man: an approach from evolutionary genetics. Pp. 133-153 in R. Fox (ed.) ASA Studies 4: Biosocial Anthropology. Malaby Press, London], Bill had a sense of intellectual closure in regard to the whole business on the evolution of altruism. What could be said about kinship theory, reciprocal altruism, and the like, had pretty much been said. The rest was a mopping up exercise that he was not interested in--it was time to do something new. (Segerstrale 2013, p. 155)The specific question why Hamilton, of all people, did not even try to find a sociobiological solution to the maintenance of sex problem was answered. The next question - why he turned to parasites and not something else? - is also answered in passages detailing how Hamilton got intrigued by parasites during expeditions. Remains the question why Williams, Maynard Smith and everybody else did neither try a sociobiological approach to the issue? But that cannot be expected from a biography of Hamilton. There seems to have been a general trend towards either ecological or mutational explanations concerning this issue. Maybe the wars around sociobiology were putting everybody off that track.