"The more shots you take, the greater your chances of sinking that basket. "
Sort of. Except I think that the effort involved in writing good essays for college apps for most students isn’t comparable to shooting baskets. It’s more comparable to doing 50m sprints pushing a weighted sled. You can shoot dozens of baskets in a row without suffering significant decline in strength or quality, but just like sprints pushing a weighted sled, most students can’t pump out dozens of well-tailored applicable essays that demonstrate their knowledge of and fit for a very selective school without suffering fatigue and declining quality.
If you have a kid that researches and writes quickly with quality and has time to do all those apps - then definitely more apps will give you more chances. Or if you’ve identified a group of colleges who values very similar things and can blanket target that way, you can also send apps to that group without much effort. But if you have a kid that is already spending 60-70 hours a week between school and ECs and also takes time to research and write polished, targeted essays, then they’ll find the quality of those essays starts to decline after a little while.
There’s another thread where a kid is asking if his waitlisting at UChicago is a hint that he’ll be accepted at Stanford and Brown. Take that set of colleges as an example. I could be wrong, but I believe those three schools - while all top colleges - are looking for different things in a student and most students who don’t research what each one of those is looking for and just writes one set of essays to send to all three is not as likely to be admitted as a student who tailors his/her essays to what each of those schools is looking for.