Oh sure, just say 'abracadabra sis-boom-bah' and you get sexuality. Tell me another joke. For one thing you need diploid organisms for it, for another you need a system to mix the features of the two sexes correctly. For another you need sexual organs, and a totally new reproductive system. Yeah sure, just 'abracadabra' does it.
This is a combination of begging the question, and ignoring the answer with a little rudeness thrown in for spice. A mushroom is I aver, quite obviously, a multi-ploidal organism in the making. Ploidy is simply a popular answer to the question, "How can I pass on the genes of a multitude of critters all at the same time. What we see in mushrooms is a sophisticated array of chemical signals that serve in a way analogous to the central clock of a computer, to align the reproductive timing of a number of organisms. It only looks hard if you've convinced yourself that the ploidy mechanism we have is the only one possible. This is obviously not so, as there are several different ploidy's currently deployed. Obviously, there was once a hefty competition in such things, and what we now see, and think of as fixed, and therefore, hard to explain, is simply the winners of the contest--the few remaining fossils, if you will pardon the conceit, of a previous competitive evolutionary paradigm.