This is a good question but essentially pillows dampen the unwanted “overtones” or excess ring created after the initial strike. With a bass drum you generally want a type of thud or punch sound that you feel in your chest. Those pillows dampen out the higher frequencies and shorten the length of the overall thud. Head manufacturers like Evans, Remo, and Aquarian make heads like the EMAD, Powerstroke, or Super Kick II that have dampening rings on them to either have smaller pillows or specific dampening material designed for bass drums.

On designing - Wood needs to be designed a certain way to produce the overall desired effect. If they didn’t make drum round and hollow there would be many issues with proper tuning and overall structural integrity. You need a cylindrical tube made of wood with nothing attached so that you, the user wanting a specific tone, can dampen and manipulate it the way YOU want.

Edit: spelling