This is just not true. Plenty of regressions have coefficients that arent statistically distinct from zero.
>But this approach cannot tells us if those inputs are drivers, much less the main ones.
Again, untrue. There are plenty of statistically appropriate ways to estimate causality. You might consider looking into the latter-day work of Judea Pearl, a well known computer scientist. "The Book of Why" seems like a decent place for you to start, because ut is for the layperson, and you have a ton of fundamental errors in your statements of "fact."
>unfortunately with media, politicians, and the general public so science illiterate that they're unable to engage with this research on its own terms
You should also add "the confidently incorrect" to your list!