Why the hell would that realization change your mind? For society at large, that "huge spectrum" includes copious amounts of superstition and ignorance, which (one would hope) should be significantly lower in those people subjected to scientific scrutiny on a regular basis. You're gambling on something being in that spectrum that will positively offset this negative, but you don't know (or mention) what it is.
"But do I want educated and principled jurors on any jury that judges me, ones with enough fortitude to mis-trial a jury or nullify a law if that's what is required? Damn straight."
So you actually want a different kind of elite to be jurors, but not just physicists. You don't actually want citizens as a whole.
"If the notion that your citizen-peers might not be informed troubles you, take time to help others form informed opinions."
Have you ever tried that? What makes you believe that your citizen-peers are even interested in spending their valuable time to listen to someone else trying to change their opinion? Lots of people are quite fond of their uninformed opinions.