>why we in the "West" for so long mispronounced (and still do) Chinese names and place-names, for example... the transliteraters were, shall we say, sloppy.<

Anna, I'm afraid I have to take issue with you here. It is not the transliterators who were sloppy, it is the transliterees. (Ooh, I knew I wouldn't get away with that one! ) Or maybe the English alphabet, which is sloppy enough that it uses a mere 26 letters for far more than that number of sounds.

Let's take "Deng Xiaoping" as an example.
In Pinyin, which is the transliteration system used by mainland China, he transliterates as Deng Xiao-ping.
In Wade-Giles, which is an older transliteration system used by Taiwan, he transliterates as Teng Hsiao-p'ing.

A student who knows either transliteration system will have a clear and precise idea how to pronounce the man's name correctly. Each is equally good in this case.

An English speaker who does not know the transliteration systems will come closer to a correct Mandarin pronunciation of his name if it is transliterated using Pinyin. It can be argued that Pinyin is a more useful transliteration system in this case.

(Neither Pinyin nor Wade-Giles as shown above show the tones of the syllables, which are integral to their meaning. Both have fuller versions, barely used in English targeted at non-Sinologists, which do indicate the tones. This is a different issue.)

So far, it sounds as if Pinyin is an improvement on Wade-Giles. And it probably is, for Mandarin to English. But Mandarin to English is not the same as Chinese to English. Chinese includes all sorts of other dialects/languages, including Cantonese, Fukkienese, Taiwanese etc. Some of these dialects (and I am reaching the edges of my knowledge, so don't quote me, but I am pretty sure Fukkienese is one of them!) distinguish three consonant sounds where English only distinguishes two. The Wade-Giles transliteration preserves these three distinctions. The Pinyin (being a construct of the Party who also wanted everyone to speak Mandarin rather than their local language) makes no allowance for three consonants.

Example:
Wade-Giles b - soft, unbreathed (try saying b without letting any breath out of your mouth - that's the nearest I can get to an English equivalent!)
Wade-Giles p - soft, breathed (equivalent to English b, Pinyin b)
Wade-Giles p' - hard, breathed (equivalent to English p and English p)
Similarly, there are three sounds in the g-k continuum and three sounds in the d-t continuum.

Now, if you're a student trying to learn Fukkienese (or Cantonese, or Taiwanese, or any other language that has three consonant sounds in the series instead of the two that English has) which transliteration system is better?

Remember, the systems were designed for students of the Chinese language(s) in the first place!

My main point is, I think it's a bit unfair to say the early transliterators were sloppy when in fact they were trying to devise an English-letter system that could represent more distinct sounds than the English language recognises!

PS, If you find the concept of the three different consonants b,p,p' difficult, don't worry. It took me about four years to get my head round it and I was meant to be studying the stuff!