My understanding is that the main reason for different sexes in Fungi is to figure out whose mitochondria go on to populate the child after the nuclear DNA is c

My understanding is that the main reason for different sexes in Fungi is to figure out whose mitochondria go on to populate the child after the nuclear DNA is combined. Having mixed populations of mitochondria inside a cell would provide an incentive for competition among them, which would be a Bad Thing. Otherwise they fungi could just do away with sexes entirely for a further, much smaller, increase in the number of potential partners. See Power, Sex, Suicide: Mitochondria and the Meaning of Life by Nick Lane.