The pillow is there to dampen the resonance of the drum. If you have a drum with no pillow and hit it there will be a long ringing "boom" tail to the sound. Then if you put the pillow inside and leaned it a bit against the other side of the drum (That head is called the resonator or resonant side, the side you hit is called the batter) before hitting it again you'd remove that long ringing tail and the drum would sound like more of a short "thwack".

They aren’t designed to not need one because each percussionist likes a slightly different sound. Without a pillow it’s like a mini upright bass drum, so some damping is needed. Some people like a bit of resonance, some people like a quick thud. This will change not just from musician to musician, but also from venue to venue and song to song.

When you strike the drum it'll create a wave of sound inside the drum. Normally this wave starts bouncing around inside the drum, back and forth, giving a sort of lasting ringing a few moments after you hit it. That's not usually want people want, they want the sharp WUMP of the drum, and then silence.

So the pillow as an a "damper". To damp something is science-speak for "reducing the intensity" of something. In this case, it's reducing the intensity of the wave so that it dies quicker.

Not to be confused to dampen something, which means to make something slightly wet.

It's for when their feet get tired hahaha . It's actually for dampening and changing the sound of the drum .

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

So why not design some thing where when you flip a lever you'd get the pillow effect? Flip the lever back for normal drum.

They have… it’s called a digital set.

Nobody wants an open drum. Everyone just wants different pillow effects.