"Since we already have symbols for all the sounds we can pronounce"... Not with 26 letters we don't. Other languages have other sounds that English can only try to emulate, and even English has sounds that require multiple letters.
It does not include sounds which are borrowed from other languages, like the Hebrew 'ch' which happens at the top of your throat, or the Spanish trilled r, or the glottal stop which actually occurs in spoken English all the time in some dialects.