I put most of my tips on myself and leave them thick. I like a softer hit and even with a pretty hard tip, like Triangles, if they are left thick, the hit is quieter and softer.
Almost all the strong players I know like very thin tips. One guy, when he looks at my tall, thick tip, says it almost makes him sick at his stomach to look at that tip!
My theory is that thin tips are somewhat of a FAD with good players. Regardless of how the trend started, somehow it has become "the thing to do" among strong players. When I started playing pool back in the early 1960s, I don't think thin tips were the "in thing" among strong players, but now they are.