That is basically what I was trying to relay: That the choices of letters were picked to represent something "different but close enough", borrowed from alternative Anglicizations that were close at hand.

>Those sounds do not exist in English, hence English speaker cannot hear or pronounce it correctly.

I never had a problem differentiating between the 'q' and 'ch' sounds in Mandarin, and I do not think I am uniquely gifted. Listening to a native speaker pronounce Chongqing for the first time made it immediately obvious. I remember struggling a bit with pronouncing 'zh-' but not because I couldn't hear a difference, it just took a little time. And even despite taking a while to learn the pronunciation, I never struggled in hearing the difference between zhuan and juan.

One doesn't hear letters (or characters for that matter), instead one hears articulations, diphthong, glottal-stops and so forth. I guess you could try to mediate what you hear through an unrelated written language, but that seems like counter-productive extra effort.