To use your slightly unfounded metaphore... you certainly don't need an electrical engineering degree to plug in and use a toaster, nor do you need a music degree to listen to a stereo.
You don't need an electrical engineering degree to put together a toaster, but you need the knowledge of a technician in order to do it; neither do you need a music degree to play or sing a song, but you need at least the basic training of how to do it. The more pieces you know how to put together, the better you'll do (at either job).
You do need a basic understanding of electronics to design a toaster. If you have really deep understanding of electronics, perhaps you can design a radio or computer. Similarly, if you have basic understanding of how music works, you can certainly design a song or play a riff around a chord - if you have much understanding of music theory you can create your own songs.
With both professions, the more you know - the better you'll be able to do what you do. If you know why music exists, perhaps you'd be able to bring music to an entirely new level. The guitar wasn't a god given instrument (nor was the calculator) - someone had to come up with it, and there has to be a reason they did.
Everyone has their own strengths - if one person's is math, but another's is performance, who are you to say how they should go about learning music. (After all, music is just an application of the science of sound - and all science is based on mathematics).
