Intuitively I'd think that if I want to find the "best" set of parameters, I can simply take the best performing 1 guy from a subset of lots of children, make that guy generate 100 children similar to himself, pick the best performer and repeat. What purpose does it serve to pick specifically the best 2 and crossbreed? For that matter, why not select 3, 4, or 10 parents ("orgy-derived" zygotes) from which to create each generation of children?
"from a subset of lots of children" - how were those children made, and what mechanism makes them different from each other? "generate 100 children similar to himself" - if not exactly like himself, then what mechanism makes them similar, yet not identical?
Sexual reproduction is a mechanism that answers these questions. Through sexual reproduction you create new combinations, made up of the genes of fit individuals. Just using random mutation alone as a mechanism for creating diversity and new combinations is what it says - random - a shot in the dark. Sexual reproduction creates new combinations using the genes of successful individuals, which is not simply random.
Questioning which is better, sexual vs. asexual is a good question, and there are a lot of articles on this topic of sexual vs. asexual, and not all favor sexual. There are successful asexual mechanisms, although I'm not sure if the alternative you proposed in your question is among them.