I think I would have to be in the consequences camp. I like my sex to mean something. As people say a lot on here, people come by for adult games, which are more than just porn. You can go anywhere and look at people having sex, there are pictures and videos of massive loads, giant boobs, hyper pregnant women (and men) and orgies that would put the most debauched roman hedonist to shame. But people come here for games, that means player agency and story telling.
It's more than just getting pregnant or impregnating a picture, it's doing that to a person. There are some games that do treat this lightly, and while they are inferior in my opinion, but it does make for an interesting score counter. These tend to be male MC focused games, which certainly leans into the desire to spread ones seed. I'm not sure I remember any female MC games that treat it as a pure score counter, as in those cases you kinda have to actually deal with the pregnancy...
Pregnancy is by general accounts unpleasant and raising a child is obviously quite the commitment. When a player or character chooses to undergo that for another character or even if they have it forced upon them (willingly or otherwise) they make that commitment. As an act of love it can be powerful, as an accident it ties the two people together, even as an act of hate things to a new level. The pregnancy takes any emotional aspect and brings it to the next level with the mightiest of narrative elements... consequence.
Even just as an act of instinct, raw breeding, it changes the emphasis of what the sex is about. The characters are demanding consequence.
Then games allow you to explore the repercussions of that, decide how you will treat the people who got you pregnant or who you impregnated. What does this change? These are all powerful themes all too often brushed off with a one slide pic of a girl with a bloated belly during an ending. Happily ever after, your going to be a parent. It's such more fertile ground than that... (pun intended)
(Post pregnancy game dev disclaimer: My game will have pregnancy themes exploring these, but does not yet... early days and what not. If you don't know the characters pregnancy is less meaningful.)
Incest is something similar, even just the tag turns an otherwise out of context picture into a whole story. Then due to the inherent taboo of it that increases the emphasis of any act between the characters because it is beyond normal. This is probably why it pairs so well (and often) with pregnancy. The characters aren't just having consequences, but dangerous forbidden consequences that society could look down upon.
From the narrative perspective there is just a lot you can do with a relationship that is wrong by default. Because most stories are about the overcoming of obstacles, in this case you can naturally tell a story with interesting conflicts despite these strong attractions. Like telling stories about exploring sexuality platonically, because you can't possibly love your brother... not that way!
On top of that there is a natural attraction to people you know, in family this is generally counteracted by an opposing force of classifying them as "just family". This is why you are often interested in people you know well, regardless of any starting physical attraction. In the case of relatives who longed to meet but were estranged it is relatively common (with a capital relative... in both meanings) for their relationship to turn sexual as their attraction is strong but they never grew the counteracting familial bond. This can be why so many people are interested in the relationships, imagining someone they have known for all their lives and that bond turning sexual. Also one of the reasons why this can be such a fantasy only fetish, like you like it but you'd never do it to the actual people you know... a hot cousin turns up though...
(I am obligated to say that I do not own nor endorse any third party patches for my game)