But this is with only one gene. Imagine there are five a, b, c, d and e. An individual with all five will arise much sooner in a sexual species.
The evolution of sex isn't a mystery any more than an eye is a mystery. It's not all or nothing. Life didn't go from bacteria to peacocks in one step. You can have something like optional hermaphrodite sex (in mollusks, I think) where you can exchange genes when the conditions arise, but it's not mandatory. The costs are virtually zero, but the benefits are still there. But then it becomes advantageous for idividuals to cheat and impregnate others, without producing eggs themselves and you get separate sexes.
And yes, once you get to more mutations then sex is more advantageous for a number of reasons. No one is claiming that sex is not better over long enough time scales. The question is how can it be advantageous enough to become fixed in a population over the span of a couple generations.
And yes, sex did evolve gradually. Slime molds have optional sex (and more than 2 sexes!). But still keeping the machinery around is expensive. One would expect that individuals that ditched it would outcompete those that kept lugging it around unless there was a relatively short-term benefit to sex.
It doesn't need a long timescale, asexual species get out-evolved by sexual species and go extinct eventually. Sexual species have a much higher probability of entering new niches or surviving when the conditions change. This can be seen in many species that reproduce asexually when the conditions are good, but reproduce sexually when stressed.
A species that loses the ability to reproduce sexually is doomed to extinction. Asexual reproduction is essentially putting all your eggs into one basket. When you die of a disease for example, chances are that most of your offspring dies as well AND there is a much higher chance that the disease adapts to your genome in the first place. This can be seen in agriculture, where plants are reproduced asexually to a much bigger extent than what would happen naturally. Many are impossible to grow without heavy doses of pesticides, as the diseases quickly adapted to the commonly planted strains. The strains need to be replaced every few decades, before growing them becomes essentially impossible, even with pesticides. Evolution is much faster than you assume.
Scale this up to 1000 individuals, each with mutations that are advantageous or disadvantageous, which impacts their chance to have children, and run it across a few generations (with a small chance of children getting new mutations not in their parents), and the chance of a subset of the population getting many of the positive mutations is much much higher than if they were an asexual species.
The asexual species will end up with more member of the final population having the single most advantageous mutation, but with none having more than that.
2 parents can have more children than 1 parent. Hermaphroditism means twice as many offspring with 1/2 as many copy's of your DNA.
Even single celled organisms will exchange DNA.
This arithmetic becomes ugly fast for asexual reproduction.
On the other hand, in a sexually reproducing organism, a disadvantageous mutation can be masked if recessive, and selective pressure will only remove homozygotes from the population. The end result is that harmful mutations can stick around for a long time, and even accumulate in individuals.
In asexual case, an individual with one advantageous mutation and ten slightly disadvantageous will be flushed out.
In sexual case, such individual will produce some survivable offspring and the advantageous gene has good chance of flourishing in the population.
A lot of insects can reproduce asexually but they are also capable of sexual reproduction. Ones who are not eventually die off.
And yes, optional sex is almost certainly how sexual reproduction arose. Even today I'd wager there are more facultatively sexual organisms than obligate sexual. That's a non-sequiter, though, as even optional sex would be bred out of a population if it could not show a benefit in a small number of generations.
It could have involved very unlikely events.
It's obvious how a sexual plant that is able to obtain the beneficial mutations from the other two populations would gain a major and immediate advanage.
This paper presents a hypothesis that explains how sexual reproduction could be more advantageous than asexual reproduction after one generation. This is what makes it novel and new.
It's two generation with or without selective breeding. The first generation will have individuals with three or four beneficial mutations, the second will have some with five. (assuming the traits are dominant)