First, it needs to be said that incest in popular culture is prevalent in many other culture. It isn't unique to anime or manga works. Although it is true that compared to Western comics it is less prevalent, incest do exist in Western pop-culture songs, movies, literature, etc.
With that, we should focus on what it is in Japanese culture that makes incest a seemingly prevalent trope in anime and manga. There's also different types of incest relationships.
Incest is a taboo in Japan. What is incest to them, however, may be a little bit different than ours. Incest marriages between cousins are occasional as they are not considered incestuous until recently. This may explain why incest relationships like in Elfen Lied is a recurring trope.
Another thing is that historically, marriages between nephews and nieces have been approved. Even now in some rural areas, fathers marry their daughters when the mother dies. They are forced to do this as they follow old feudal laws. Sometimes when both parents died, the brother ends up having sex with the sister in order to end confusion.
There's also the common trope of brothers and sisters sleeping or bathing together in anime and manga. This is easily explained as such things are still prevalent in Japanese society. This doesn't necessarily lead to incest, however, but there are certainly hints towards it.
The first manga that involves incest is Cream Lemon, released in the 1980s. So this isn't something new. It is also noted that incest is in mangas for the Shoujo demographics, which is mainly for females. In other words, people might like incestuous anime and manga for the emotional relationship and not the physical relationships.
The combination of Japanese history and the demographic's tastes may help explain why incest is a popular trope in anime and manga. I could go on and on, but it may take too long to explain, so if anyone would like to read more, I have provided sources for others.