Yes, “it can be said”, but that does not mean it is correct. At the same time, I am not making the point that it is necessarily wrong.
Even if ‘typical’ is used to work out “the commonalities of the majority of the human race”, that is not what per se takes this ‘working out’ any further, and my problem here is that moving from the assumption of hardwired moral predispositions, as well as the assumption of absolute “reason and mind”, is not moving in any direction I may find convincing.
“Nurturing the newborns” is what mammals do. Using your example, that may lead to the the inference that humans are kind because mammals are, and hence human kindness would be a void or nugatory concept. It would not even be “human, all too human”, but instead “mammal, all too mammal”.
It could be more ‘human’ if we consider that the children of man are incredibly weak and totally unable to self-sustain for a considerably long period, years in fact (if ever in this age…). The species would have almost certainly gone extinct, if humans had not developed social patterns to nurture and protect their helpless offspring. In Africa (not sure) they say it takes a village to raise a child. So “human kindness” could have developed exactly because also non-parents care about infants. Yet, I do not believe that this “kindness” is an evolution by-product peculiar to humans, at least with respect to newborns (because “kindness” to babies, even when those do not belong to the same species, has been often observed in wildlife).
Nevertheless, I am still inclined to think that what you label “human kindness” has its root in the social interplay and not in any phylogenetic trait.
The paradox here is that whenever we consider a more developed, complex, anthropically modified environment, where references to wildlife and other animals progressively lose relevance and heuristic value, then the defining trait may well turn out to be no longer kindness. Or proper “human kindness” would be only what you name “prescribed kindness”, which one could also call ‘hypocrisy’. Instead, the peculiar human character that could be observed in such uniquely human environments would be something most people consider to be the opposite of kindness: cruelty.
Use of cruelty as a policy tool, a systematic, bureaucratic cruelty, like when Herod ordered the massacre of the innocents, or the systematic killing of enemies, maybe after sorting out them in groups, so that some would be executed immediately and others enslaved, or the use of capital punishment to set examples and inspire fear of the rulers and of the laws, etc., all that is indeed very human. (Actually, that is not so true. Cruelty-based policies appear not to be uniquely human. I would only say that it is legitimate to entertain the idea that this usage of cruelty is as the core of large human organisations).
And coming to mind and reason… the refinement of spirit in general, that too can - and should - be seen as cruelty.