I think it's because social interactions are far more complicated than combat. In most games, it doesn't matter how good I am at shooting, swinging a sword, or swimming it only matters what's on my character sheet. With social skills, how effective the player is at communicating can often make a significant difference. As a DM, I've committed the cardinal sin by letting how good the player is at communicating help or hinder what they were trying to accomplish in the game. These days I try to do my best to remember to say, "What are you trying to accomplish?" in a nice and friendly way.
I don't think social interactions are more complicated than combat. This looks like an ingrained assumption due to being very familiar and comfortable with the abstractions inherent is combat engines (5e in particular). However, even if you're going to assume this, then why would a game have less support for a more complicated interaction than it does for a less complicated one? This argument leans towards just saying that social interactions are too hard to even try to model, so the best methods are ones that have no structure or teeth. This, of course, is ignoring that there is still a game mechanic that is defining social interactions, and it has teeth -- the GM decides. You've ported any responsibility for modeling social interactions to having one person imagine what's possible and preferable.
I think this is a large impediment to a number of these conversations -- there's a set of assumptions attached to play due to long experience and received wisdom of D&D. These manifest often in statements like the above -- that the multiple levels of a combat, even between just two people without magic, is somehow less complicated than a negotiation or haggling interaction. I can't say which may or may not be more complicated, because both are hideously so, but I think that they're pretty close -- especially for RPG purposes.
As I said in a different thread (I think), the mechanics of game really need to be evaluated in the light of what you're actually asking them to do. And this posing of the question is where I think that things go off the rails in games that don't really lock it down clearly. In 5e, for instance, how you make a check is straightforward, but what question a check answers is not at all. The scope of questions posed to the 5e mechanics from all the different GMs is very broad and often not even thought about. The question posed is very complex, because it not only deals with what action is being attempted, but also what the consequences or rewards are. These are, quite often, skipped until after the check, because 5e defaults back to GM decides and the GM is really using the check not as a resolution mechanic but a decision aid. This is why you'll often see things like giving a better resolution on a very high roll (or 20) and a very bad outcome on a very low roll (or a 1).
There's nothing wrong with this, but if this is your approach, it's very hard to accept/see/grasp what actual constraints this puts on play -- and it does constrain play. It creates an opaque, black-box decision process that players have to try to understand experimentally -- what action will the GM allow here. This can be quite a fun experience, mind, but the constraints of play are still there as players may refrain from preferred action declarations because they know/worry that the GM is or will be adverse to such things.
The clearer constraints by a more defined system appear like they provide a smaller play space to those that are unfamiliar with such constraints because they obviously reduce how their used to playing. However, it's a case of close one door open another, because while the clearer constraints often directly restricts familiar play, it also allows players to engage in ways they cannot or usually do not in other approaches. It's not that the mechanics actually create more constraints on play, but rather just different constraints, while also removing constraints on different approaches. For example, when I play Blades in the Dark, my approach to how I play my character is very different from when I play 5e, and this is directly due to how the game mechanics allow me to engage. I face both different constraints on play and different freedoms, but I'd not say that one has more of either than the other. They're just different.