Does it make sense to talk about the 'social brain'?
Short answer: Yes, as long as by "social brain" we mean hardware adapted for handling particular "social" software.
1. (paper 1) The basic premise, that the human brain is NOT innately specified to be social, is in direct opposition to modular theories on ostensive adaptations - isn't it? Mainly due to this, I have concerns on the whole argument as it builds upon a Tabula rasa style of logic I think to be wrong.
2. Their argument that the infant brain is not a miniaturized adult brain, and hence supporting their idea that "sociality" is learned, is very weak. One can just as well argue that the fine-tuning occurring early in ontogeny is both innately specified and based on experience. For example, ostensive adaptations can be argued to solve opacity issues in social interactions/learning: they are innately specified, but the content is not.
3. The argument of deprived youngs from maternal care is also weak: just because less of a specific behaviour emerges in the adult phenotype is not a proof that there is no innate specification. This is all too reminiscent of the straw-man type of argument for genetic determinism.
4. They spelled glucose wrong in Box.1.
5. You can model mommy-infant dynamics with a Bayesian fremework, sure, but what about the priors? Those have to be innately specified. For example, the double direction of oxytocin on mother-offspring is (by definition) an innately specified physiological positive-feedback loop. One of its effects is the positive reinforcement of "social" interactions between them (mother is "in love" with the child and increases milk production + child feels physiologically conforted by the presence of the mother). I really do not see how these types of bio-chemical interactions can be learned from zero. Take other species, like the octopus who do not have mother-offspring interactions at all. Do they have such loops? No they do not. Could they learn them? No they could not. Why? Because they have not evolved a "social brain".
6. I have serious issues with the first paper. Not all concepts are just cultural/social cunstructs. For example, they mention a child raised by two fathers and no mother, and how "mommy" is a learned concept instead of a biological imperative. "Mommy" might be a learned concept, but "Mother" is not. Mammals lactate for a reason. Humans are no exception. Infants are hard-wired to seek a nipple to get nutrition in their first life-stage. Literally they cannot chew food and they absolutely depend on their mothers to give them colostrum and then milk, as it has been for millions and millions of years. I really do not see how basic biological reality of what it means to be a mammal can be socially learned concepts of a "not-social-brain".
7. They use metabolic rate as a proxy for the amount of social interactions.... I am severly against this. Metabolic rate slowing, as in their mentioned example of the sloth, serves much more concrete functions: detoxification of plant matter and energetic trade-offs (as easy examples). Animals that specialize in decreased metabolic rate have found a local solution to a local problem regarding energetic constraints, nothing to do with sociality. Take the octopus, again. They are the least possible social animal and yet have an extraordinarily higher metabolic rate proportional to their bodyweight. Why? Because they diverged from other mullusks millions of years ago in terms of survival strategy: while the other mullusks invested in tough outer shells and lower metabolic rate (low movement), the octopuses abandoned all their physical protection and opted for augmented mobility (which necessitates a much higher basic metabolic rate) and cognitive flexibility (also).
Which accounts of the social brain do you find most convincing?
I think the "social" adaptations of the human brain are not the defining features of the hominin lineage. The first significant brain encephalization occurred over 2 million years ago with Herectus, while the second with Neanderthalis/Achelian/Sapiens (late Pleistocene) complex. I believe those brain explosions had little to do with sociality, but with (1 - the first expansion) the winning of an arms-race into the cognitive niche as a weapon on par with prey/predator physicalities and (2 - the second expansion) the decline of prey size as a selective agent. "Social modules" were selected for, most likely, through both expansions, but were not the only (or even the primary) reason for it. As an example, all predators have larger brains than their herbivore counterparts (adjusted by total mass), simply because being a predator necessitates higher cognitive function than being a prey. In humans, cooperation is just one part of our cognitive arsenal, together with (e.g.) a pristine intuitive understanding of causal dynamics.
If I had to choose one out of the social brain accounts (which I barely know), then I would have to select one grounding the "social brain" on cooperative phenotypes (including the evolutionary advantages of manipulating, and being manipulated, by other minds).
In other words, I see the human brain as a "social brain" only in so far as it is specifically adapted to make use of a variety of social softwares. These adaptations are innately specified, but SOME OF THEM require external inputs during ontogeny to develop fully (one can argue this is even more efficient that having a blueprint). Lastly, some behavioural phenotypes that look "social" are in fact not so (e.g., mother-child physiology: not social even if involving 2x agents).