Great question!
Of course, an insufficient albeit factually correct answer would be that evolution is still on-going.
More to the point, however, it depends on the complexity of the lifeform.
If you were a simple organism (like a simple bacterium) your high reproductive rate allows for sufficient mutation to survive. A more complicated reproductive system is not required. Arguably, bacterial conjugation which, as a mechanism for the exchange of genetic material, is regarded as the equivalent to sexual reproduction at a single cell level, can increase the speed of mutational adaptation. But the need for increased adaptation only became urgent during modern times with its biological/chemical advancements. In simplified layman's terms - nature didn't throw a new antibiotic on the market every week. B/Conj was discovered after WWII, but we don't know if it existed in earlier times or if it is a recent evolutionary step.
The more complex the organism gets the more beneficial DNA transfer becomes, but it comes with a price: it requires a complex reproductive system and it requires a mate.
Simple invertebrates include an intermediary evolutionary step in the form of hermaphrodism: The search for a mate is facilitated by the fact that you can do it with any other representative of your species, not only 50%.
Once you get into really complex organisms you need to optimize the quality of the genetic exchange and have to forgo hermaphrodism. This is dangerous as you reduce your chances by 50%, but nature concentrates on the species and not the individual.
In case you are interested, here is an intriguing article in non-scientific literature, somewhat related to the subject: it shows how sexual reproduction seems to be superior in slow (compared to single cell system) reproductive systems.
Sexual vs. asexual reproduction
Hope I answered your question. Cheers!