It is precisely the process you describe -- that people are very prone to thinking about something for "a few seconds" and "find[ing] some plausibility in the n

It is precisely the process you describe -- that people are very prone to thinking about something for "a few seconds" and "find[ing] some plausibility in the notion" -- that makes the rationalist scientific method important in the first place. If we could just think about something momentarily to evaluate its probable truth, we would have no need for experiments, hypotheses, or sorting out correlation from causation at all. We need those things because superficial "think about it for a moment" analyses are very often totally wrong. Also note that pointing out that this correlation does not imply causation is not at all the same thing as denying that there exists a causative link between the factors. It's simply stating that this evidence, in itself, is not sufficient to establish that. Other evidence well might.