I don't always engage in this, but I'll bite.
In a neutral sense, I see the appeal of each ship you tagged; they are just not appealing to me specifically and I’m afraid I wouldn’t do them justice. I can only speak for Jaytim and I do not intend to start a debate; just explaining my own view. The moment you attempt to superpose your interpretation over mine; I will just block you.
Gotta start by saying that most of the jaytim fandom (and I know the general consensus is that this also applies to jaydick) do not see them as brothers (in the traditional family sense of the word). The “Batfamily” is not a typical traditional family but rather “found family”. Each of them met under different circumstances and they all formed a different and complicated relationship, independent from the bond they may share with Bruce.
Most of us were introduced to Jason and Tim through their early comic versions (1990s-Early 2000s, if you've read those then you’d know). They met each other in their late mid-teens in an antagonistic manner (AKA the events at Titans Tower). They are not blood related but more importantly: they did not grow up together. A family bond, whether it is blood or by adoption, is nurtured, it is grown, is built through time and care; it doesn't just appear because a paper said so. Family earns that bond through love and trust.
DC has gone back and forth, changing the legal status of Tim and Jason in respect to Bruce through decades, but it doesn't erase the fact that they (Jason and Tim) never saw each other as family in their formative years and doesn't erase the damage they inflicted on each other. Their story started as strangers/enemies. Doesn’t matter how many times DC reboots and makes changes to their own canon. They simply didn’t work to make Jason & Tim being “brothers” anywhere near believable. The only thing they truly worked up to was reluctant allies/allies at best. So, it comes down to how each person got introduced to the specific character relationship. That’s why people simply cherry-pick whatever they want from comics and interpret their relationship however they like, whether it is romantic or platonic, it simply can go in any way. It is up to each person’s preference. I dislike current continuity, so I ignore it for the most part.
The real appeal of jaytim has nothing to do with incest. Is about them making bad decisions, hurting each other, getting on each other’s nerves, riling each other up, about them being seemingly bad for each other due to their different views and past. At the same time, it is about them finding common ground, realizing they have more in common than what they originally thought, about them realizing they have both suffered and had traumas to endure. They both know that it is hard to fill the robin shoes and they both know the feeling of being replaced. Neither of them has had it easy. And for me that I love them both as characters with all their flaws: Is about them seeing what I see in them, and that they can both overcome their flaws and complement each other quite nicely. It’s about them hanging on the edge of love, hate and heavy denial. It’s about that “ah, this person is …truly amazing” and that “oh” moment of the same person realizing maybe they started falling for someone that has all the reasons not to trust them. It’s about their journey to realizing that yes, they are very much worthy of love and happiness. About forgiveness and second chances.
They both have witty personalities, hold their own against each other and neither of them backs down. They can (and do) get on each other’s nerves. To us, jaytim shippers, that’s how they flirt. For all that N52 has many flaws, it has shown that how it could look like if Jason and Tim worked together: they banter while getting things done (see Robins War and Batman and Robin Eternal). It IS because of their complicated past and their own personalities that they make an appealing couple which offers the chance to explore both characters in depth at both the emotional and physical level. Romance offers the whole package so platonic has nothing to offer for me.
Due to their strong personalities, they can either clash and burn or overcome their issues and grow together. Jaytim can be anywhere between toxic to disgustingly sweet (should they overcome their hurdles).
To me, it has nothing to do with it being seen as “incest”, especially by people outside jaytim fandom. I don't even like using the term batcest because it feels like I’m scamming people who genuinely enjoy and are looking for taboo content. Tags are meant to be useful to find things you like (or filter them out). I don’t mind people that see this as incest – at the end of the day, it is fiction, so I doesn’t matter- but I simply do not see it. On the other hand, people looking for incest and feeling baited for nothing, would be rightfully mad lol. There are people that have openly wondered where the incest content is since they came here looking for it, but it is arguably hard to find. That’s because canonically, that kind of relationship, at least to many of us, is nonexistent. DC never did it - they entirely skipped properly mending bridges and building any filial relationship between those two (unlike, for example, Dick and Damian, who had a whole book) and went directly to allies/”brothers” by name because Bruce said so, like a really shitty bandaid. So, when you build a relationship between two characters with your own interpretation, it can result in something platonic if that’s what you like, or something romantic. We simply have more fun in the latter. More importantly, it is also about the people in fandom: We have fun creating, encouraging each other, sharing ideas, learning new skills and hyping each other up because we love these characters together. We don’t waste time wondering why other people play with the same dolls in a different way. To each their own.
blakekathryn
jacobvanloon
theartofmadeline
kianamaiart
