I've got a PhD in CS. I've spent 22 years in the organized education system. Yet I'm barely able to actually understand research results in adjacent CS subfields, let alone an entire scientific discipline. It is absolutely not feasible for even a dedicated person to become meaningfully expert in a large number of fields.

> What exactly do humanities courses help me with here?

The primary loop of humanities work is critical analysis of texts written by humans. A field like history is literally media analysis, except that the media was created by actors in the past rather than actors today.

Not that "we" are any better -- we can't even get technologists (or doctors) to understand statistics. How can we hope for a general-population understanding of scientific process?

My answer: We can't. We can hope for leadership that steers the conversation in a useful direction, but democracy sometimes gets in the way of the elevation of useful leaders, and the media has no interest in promoting good (mostly boring) governance.