Date: 2022-04-26 10:00
"I don't understand why people think they have to roll their lips "all the way under" in such a way that lip thickness would matter."
In my experience, control of the reed is the most important consideration. If one uses a reed that is not totally stiff, then the lips are necessary to control the vibrational aspects of the reed, including tone control and timbre. Rolling the lips so that most of the reed is touching flesh is a part of this.
Students of mine who had thin lips seemed to be at a decided disadvantage to full-lipped individuals who had enough flesh to control the reed.
Bay Area, California