I gotta disagree with the "sexual reproduction is to promote genetic diversity".
The way you stated it made me interpret that to be that sexual reproduction arose "in order to do ____". This couldn't be more incorrect and goes against everything we know about natural selection leading to "evolution".
No, sexual reproduction was merely a set of random mutations which proved to be advantageous for those organisms. There isn't a "goal" when it comes to evolution. There is simply a whole lot of random variables that either live and reproduce or die. Sexual reproduction does offer another division which increases genetic diversity within the developing embryo but this really doesn't matter in regards to inbreeding. When sexual reproduction was "selected" for the methodology of reproduction, it simply offers more variables. It doesn't make those variables better then mitotic divisions it only casts the genetic net wider.
If we artificially made a pair of organisms that were perfect but exactly the same. You could inbreed them indefinitely without issue.
Again, the problem with mammals inbreeding is that we diverged very recently in the grand scheme of life on this planet. Insects, reptiles, and micro organisms have been here far longer and have had much more time to get rid of defects. Yes inbreeding can be deleterious for an organism but it can also be beneficial. The exact same is true of very out crossed animals. Either the bad genes align up or they don't.