@lookingforward I think we can agree that candidates should not apply to just one school. I also think we can agree that candidates should of course try to maximize their probability of getting into a certain college (as you say by finding a “match” and being savvy).
We also agree that if the conditional probability of acceptance to each reach school is near zero (what you mean by a kid without the stats or ECs), then applying to more of them won’t help the overall acceptance rate much, since it will still be near zero.
Also, if the conditional probability of acceptance to each reach school is near certainty (like the Houston senior who got accepted to 20 reach schools), then applying to more of them won’t help, since the overall probability of acceptance is still essentially 1.0.
But there is a middle ground, where the conditional probability of acceptance is reasonable but not certain. The middle ground (which is what people loosely mean by “matches” as opposed to “reaches” or “safeties”) is going to be different for each candidate. In that case, I do think it is rational for that candidate to apply to multiple colleges where he or she has a reasonable chance of acceptance, depending on the effort and cost involved in applying, since there is always an element of randomness, even if you think you’re a pretty good match for a given college.