The main function of the Y-chromosome is to regulate male fertility, including testes size, sperm count, sperm motility, and possibly also (perhaps indirectly) the bias towards more male or female offspring. Indeed a higher sperm count or motility has been associated with increased chances of fathering boys rather than girls.
This may well explain the success of some Y-DNA haplogroups over others. Wars and conquests are not the answer to everything. If some lineages produce more boys, in a mixed population of haplogroups, given enough time they will become naturally dominant and eventually replace other, less competitive lineages.
Some Y-DNA haplogroups, or mutations found within specific regional subclades, have been identified as a cause of lower male fertility.
Haplogroup E1b1b has a higher incidence of azoospermia in Italians