That's the basic idea but single celled organisms can and do directly swap DNA segments at any point in their life cycle. Unfortunately, multicellular can only meaningfully swap DNA when they are at the single cell stage. So sex is simply the maximum DNA exchange possible while multicellular life is at the single cell stage.
The disadvantage to sex is you need vary similar organisms so your N^2 ancestors becomes (species population size) * number of generations. Where direct DNA exchange can cross DNA from far less compatible organisms (~total life population size)
The disadvantage to sex is you need vary similar organisms so your N^2 ancestors becomes (species population size) * number of generations. Where direct DNA exchange can cross DNA from far less compatible organisms (~total life population size)