I think the most you'll ever see is the use of zhuyin or tone-specific symbols as a shorthand form of writing, but not to replace characters entirely. Hanzi are too culturally important (they are what keep the dialects together) to be done away with entirely.
You mean fāngyán, right? For that, I prefer the late John DeFrancis' translation of the term, which is "regionalects". Besides, I could see something like bopomofo (if not exactly like it) in a way similar to kana in usage, to complement the characters. The characters themselves, however, seriously need to be standardized (just my opinion), which could also be done - say, the Qin reform was seen in TTL as not going far enough.
Oddly.
They write t.eg. 'wan' in english characters then a selector thing appears as they type showing the possible symbols pronounced wan which they then select.
Like this?
That method is mostly used by non-native Chinese speakers. In China itself, the more popular system is Cangjie (named after the mythical inventor of Sinograms):
Isn't that also used in Taiwan?
Perhaps this explains why alphabets have never become popular in China. The high number of one sylable words creates a large number of synonyms. Which could get confusing without the context and tonation provided in verbal speach.
It could still be done, however - witness Vietnamese, for example. It just would be a bit more difficult - if tone is taken into consideration, I've seen estimates ranging between 1,200-1,300 syllables with tone in the whole of Standard Mandarin Chinese (the amount would obviously be lower if tone is disregarded). Just remember that virtually all the alphabetic systems, with the exception of Pinyin, used in the Sinosphere were developed by missionaries - if a non-missionary romanization could be developed in TTL, that would be a feat unto itself. In the meantime, we might content ourselves with standardizing the characters and adding in supplementary phonetic syllables, à la kana.
Besides, creating any sort of alphabet/syllabary immediately kills the Chinese language - and creates a dozen new ones 'Mandarin', 'Cantonese', etc., etc.
Again, not necessarily if the characters had continued to be standardized beyond the Qin reform.
I think that for a Chinese empire, keeping a 'Chinese' language is probably very important.
[edit]even if it's only in a printed form - but that's how messages come from the court anyway
True - a counterpart to this could be seen in Arabic.
I believe they alphabetize based on the order in which the character strokes are drawn.
Which is largely through semantic classification, either through the traditional system of 214 semantic "radicals" or Xu Shen's 540 section headers. In his book The Chinese Language: Fact and Fantasy, John DeFrancis mentioned that there have historically also been phonetic classifications for Chinese characters, including the phonetic reconstructions by Bernhard Karlgren and a system devised by yet another missionary that used 895 characters to classify them based on phonetic value - which is actually slightly larger than the system for Yi, which has 819 characters arranged in a syllabary.