The main reason I make thin points on video is because 90% of my questions are some version of, "Can you show me how to create a thin arrowhead?"
In reality, most projectile points are not thin. The ratio of width to thickness is about 4 to 1 or 5 to 1. "Thin" points start at about 6 to 1 and go all the way to 12 to 1, or something like that. There are points that are thinner, but they are extremely rare.
In areas of the country where high quality knapping material can easily be found, thin points are common. But this doesn't explain the "why?".
The best explanation I've seen is that thin points have more value. They are easier to cut with, they are easier to sharpen, they are easier to notch, they snap off in the wound (sometimes an advantage for fighting/hunting strategies), and they reflect well on the knapper's skill.