I've been thinking the same thing actually.
Not that I think we necessarily need more lawyers per se, but rather, just a culture that places more value on the type of thinking and communicating that lawyers are trained to do.
So for example, we could have it be standard for all applicants to any type of college or grad school to take an LSAT - rather than just law school applicants. Or we could have one semester of high school English be dedicated to LSAT-style logic.
If we incorporated formal reasoning skills into our standard, public education, and thus normalized it as the default, best way to conduct all discourse, it would be of great value to our society I think.