Is Sexual Reproduction Important?

In today's world, producing offspring sexually is very important to the survival of a species, and there are several advantages of sexual reproduction. First, sexual reproduction helps reduce the chance of mutations. In an analogy, there is a manuscript that has been copied over and over by monks in two distant monasteries, leaving more chance for mistake, whereas having sex is like two monasteries copying each other regularly and frequently replacing their versions of the manuscripts. Mutations can be very harmful to species who don't produce sexually, suppose there is a threshold of harmful mutations an individual can carry, in sex the mixing of genes gives some creatures harmful mutations, and these creatures are quickly killed off, leaving the population safe, but if there was no shuffling of genes, the population would be overwhelmed by harmful mutations, therefore going extinct. In addition, over time organisms that don't produce sexually will, over time, be lead to several mutations, and if the last individual, that is not mutated, does not produce offspring then the population eventually goes extinct. Finally, since organisms that do't produce sexually have very similar genes, parasites and viruses, can easily infiltrate their defenses, killing them of, but sexual reproduction helps by mixing genes and making harder for parasites to kill of the species, creating a moving target. Although sexual reproduction is important and necessary, could it be possible for asexuals to thrive and grow, or would it be impossible in the conditions of today's world?