Apparently there are about 7 million oocytes created per generation[1], which could be done in 23 divisions: 2^23 = 8,388,608
So first, it doesn't require that many divisions per generation of human. Second, there are "errors" that get passed on to the offspring. Third, a lot of selection goes on so that only fertilized eggs without huge issues will eventually be born.
Right, but it would seem like many such strategies could be applied to somatic cells. And we also know that there are complex organisms that don't meaningfully age.