The obvious counter argument to the genetic book of the dead would be that our genome, rather than being an append-only log of our evolution, is a snapshot of our current morphology that is constantly being overwritten.

There simply is no history because the overwrites delete what was there before. If we evolve wings then our arms=arms gene gets deleted and replaced with a arms=wings gene?

That is clearly not how Dawkins thinks of it but I wish he had explained why the genes-as-mutable-variables model is wrong.