Why does sex exist?

[Tellos Athenaios]

Despite all its advantages, sexual reproduction has one obvious disadvantage

No, plenty of plants and animals reproduce sexually without sexual selection in that sense (think grasses, corals, etc.). Sexual selection occurs with direct insemination, and direct insemination is such a major improvement in efficiency that it is worth the hassle of sexual selection. Additionally direct insemination is also by far the best bet for sexual reproduction in arid regions because it compensates for the primary drawbacks of sexual selection (the risks from exposure to a hostile environment for eggs and sperm).