dolls by design cannot move without someone external to them moving their limbs, so even if a living doll character can move on their own, they still implicitly have this relationship to others where they not only cannot resist being touched (and by extension controlled), they cannot do anything at all otherwise. dynamics of power and control are often eroticised, and doll joints immediately mark a character as slotting into this kind of dynamic, similar to how maid outfits are sexy to some people because of the dynamic of servitude they signify. this is the main point that the vast majority of self proclaimed doll enjoyers seem to latch onto, doll joints as visual shorthand for a dynamic of dependency that may or may not be sexual.
dolls exist to entertain someone and be loved by them, their sole purpose is quite literally to look pretty for their owner. this too is a popular erotic dynamic even when no dolls are involved. dolls are artificial creations, so a doll inherently exists the way it does because someone wanted it to. in some cases this is extended into its reverse: a doll does not exist without someone wanting it to, therefore, the doll is wanted because it exists. the very fact that the doll exists implies a fascination with either the doll itself or the one it's made to look like, because without this fascination it wouldn't exist to begin with. the doll exists to be loved, so you desire it by virtue of its existence, and this gives it a certain power over you despite its powerless nature. the most common cursed doll in media is one that is resentful over being abandoned. the desire for another is inherent to dolls and this is, obviously, erotic.
in my experience this is usually the angle when you're dealing with a sorcerer that made themselves a doll body or something like that. the tension between the doll and the force that moves it is resolved by having these be the same entity, so they're a doll to signify fascination instead, be it from or towards the one inhabiting the doll.
dolls are often associated with being fragile and delicate, especially the ball jointed type that living doll characters will usually invoke. they have to be touched in order to act, but cannot be touched without risk of breaking this precious delicate object. this tension of a body that both invites and discourages being touched is also erotic.
a doll's body is implicitly delicate, but it is also a body that can be repaired or replaced when it breaks. you can completely dismantle a doll without actually harming it, and in fact dismantling it is necessary to fix it in case it does break. a sentient doll's body would logically have to experience itself differently than a human flesh body. since you can open up and pull apart a doll in various ways without actually hurting it, there are naturally various ways to touch it erotically that you could never do with a living person, and because the doll by definition exists for you, this touch can be as painful or pleasurable for the doll as your proclivities dictate. for some reason fucking nobody on pixiv seems to agree with me on this point but this is a big one for me personally, the unique ways of interacting with doll bodies as extension and expression of the way a doll's body inherently has a complex and contradictory relationship with being touched. we're talking about a body made of gaps, go stick something in those for fucks sake.
a doll allowing itself to be taken apart to be repaired (or to have freak sex) is an incredible display of trust similar to that of robots letting you poke around their circuitry. it's an emotional intimacy that's only possible with this kind of artificial partner. the capacity for and necessity of occasionally being completely taken apart and reassembled to continue functioning, of exposing yourself entirely and putting your trust in someone's deft hands, is obviously erotic.
a doll cannot exist independently, and while its purpose is to be loved, it's rare for it to be thought of as an independent actor by anyone other than children. also, if the doll /isn't/ loved it becomes completely helpless, because it needs someone else to move it, be it literally or metaphorically. a living doll character will, sooner or later and thematically if not directly, have to contend with the fact that this is a horrifically stunted existence for a sentient being to have. a doll cannot meaningfully resist anything that is done to it, and its only blessing is that it has a body that can endure this. you can violate dolls both physically and emotionally in ways far more invasive than with a real person, and depending on your angle their very existence as a doll is a violation in itself, something that lends itself well to the overlap between horror and eroticism. this is another favourite of mine that I barely see reflected in what other people are cooking up in my field of vision.
even if a particular doll character doesn't tick any of these boxes regarding characterisation or relationships, the fact that they have doll joints anyway is a constant reminder of these associations, and this contrast is alluring in itself. independence does not come naturally to a doll, so a doll that acts freely is fighting a constant battle against its own nature. this is hot and extremely underutilized.
being denied agency because the material reality of your body makes you dependent on the goodwill of others is an experience many real people can relate to for a wide range of reasons, so living dolls are useful abstractions to explore these experiences and reframe these limitations as something that makes you desirable. unfortunately this leads to most of the dollposting on this site being really boring to me because its all like "what if i was cute and loved and didn't have to think for myself" instead of the horrific violation and unique physical experience parts that i'm personally interested in, but it's undeniably a major contributing factor to general doll enjoyment.
the presence of doll joints on a character invokes a relationship to the body and the people around them that lends itself well to various popular erotic dynamics, and which marks them as object of desire not entirely unlike how a womb tattoo marks someone as primed for fucking except for people who can't get off without metaphors. im sure for a lot of people it's really not any deeper than "it looks nice :)" and that's fair, I'm a pretentious elitist who thinks most people producing doll fetish stuff are boring about it though. stop drawing regular sex with more lines and stick your fingers in there NOW