Actually, the real problem with incest is not the genetic defects but the lack of genetic diversity. I've experienced this first hand while implementing a genetic algorithm.
The problem was given as a list of inputs and their expected outputs, and the goal was to find a program that will produce the expected outputs when given those inputs. Starting with a bunch of random programs (made of a bunch of individual instructions), select the best individuals (the better they performed, the more likely they will be selected), have pairs of them produce offsprings, and mutate the offsprings at random.
Not all programs are valid. For example: "A +" is obviously invalid, because the "+" operator expects 2 inputs. Genetically speaking, we could say that those programs have genetic defects. So I tried to implement the algorithm in such a way that the starting population (which is random) was always guaranteed to be valid.
I rarely got a perfect solution (a program that would always produce the expected output, no matter what the input is), but I still managed to get perfect solutions from time to time. So I tried to ensure that the programs always remain valid no matter how they mutate or how they are combined to produce offsprings.
As a result, my algorithm became unable to produce any good solutions. As a final attempt, I decided to not bother with defects. If the programs are invalid, let them be invalid. Suddenly, I got about 20 times as many perfect solutions as during my first attempt.
Based on my findings, I theorize that guaranteeing validity of the programs has led to a reduction in genetic diversity. I essentially implemented incest without even being aware of it.