Sex is not an option but a requirement: a large genome cannot be maintained by picking up loose DNA, so eukaryotes were forced into it.

If you’ve got a small genome, the chances of you picking up the right bit of DNA from the environment is much higher than if you’ve got a genome of 20,000 genes. To do that, you’ve effectively got to be picking up DNA all the time, all day long and nothing else, and you’re still going to get the wrong DNA. You’ve got to pick up large chunks, and in the end, you’ve got to line them up, you’re forced into sex, to coin a phrase.