Why do genitalia serve this dual purpose? Is there some payoff or benefit for these organs to provide both functions of waste elimination and sexual reproduction?
Surely it's not just coincidental.
Unlike lower invertebrates, we have separation of ingestive and excretory openings. It also makes sense to have the fewest openings from the outside to the inside (the digestive tract really provides a closed tube through the body) so that the potential for infection penetrating the body cavity is reduced.