If my own judgment is so faulty that I choose to let somebody else do all my thinking for me, then how can I even trust the thinking behind my choice?

As you explain so clearly here, the point is to think for ourselves instead of trusting in any person or system. This valuable insight can be reached by many idiosyncratic paths through life. Your personal path to it, trusting too much in Science itself, is an ironically interesting one, unlikely to be trod by most. That's why your line "Science Isn't Strict Enough" fails to resonate with some readers.