I'm not sure I agree that the best mapping of Pinyin "e" is to the English "u". To my ears, Chinese "he" sounds closer to (non-American) English "her" than "hu

I'm not sure I agree that the best mapping of Pinyin "e" is to the English "u". To my ears, Chinese "he" sounds closer to (non-American) English "her" than "huh". Same for "chen" - "chun" captures neither the Chinese phonemes nor the English spelling. I'd argue even "Cheng" (hard e) is less likely to cause confusion/disrespect.