seems highly concerned with crafting and extending those narratives and distinctly unconcerned with grounding or verifying them;

I think this is a problem, BUT it wouldn't be a problem if we had more people willing to pick up the ball and take these narratives as hypotheses and test/ground them. I think there IS a broad but slow movement towards this. I think these narrative-building cultures are fantastic at generating hypotheses, and I am also sympathetic in that it is pretty hard to test many of hypotheses concretely. That said, constant criticism and analysis is a (sub-optimal) form of testing.

Historians tend to be as concrete as they can, even if it's non-quantitatively. If an art historian says one artist influenced another, they will demonstrate stylistic similarities and a possible or verified method of contact between the two artists. That's pretty concrete. It can rely on more abstract theories about what is a "stylistic similarity" though, but that's inevitable.

I also think that the broadest and best theories are the ones you see taught at an undergrad level. The problems you point out are all more pernicious at the higher levels.

There's plenty of rigorous analysis of issues involved in social science out there; it's just that most of it doesn't come from social scientists. Some of the best sociology I've ever seen has been done by statisticians.

Surely true. But I think (from personal discussions with academics) there is a big movement towards quantitative and empirical in social sciences (particularly political science and history), and the qualitative style is still great for hypothesis generation.

I also think our discussion is getting a bit unclear because we've lumped the humanities and social sciences together. That's literally millions of researchers using a vast array of methodologies. Some departments are incredibly focused on being quantitative, some are allergic to numbers.