A Chinese alphabet? It can debated as to how well a Mandarin speaker can understand written Cantonese, but the fact remains that there are SO DAMN MANY words that sound exactly the same that an alphabet would fuck the language's comprehensibility up totally. Chinese characters depend on the picture, not so much the sound to convey meaning; this is particularly true in Classical Chinese which is quite cryptic as it leaves out so many modern particles.
The reason why Japanese needs a supporting script (kana) to go with the kanji is because Japanese has declensions and particles that Chinese doesn't, so it's needed to form endings for the kanji. IIRC Japanese used to only use Kanji but then kana evolved. I doubt they really needed to introduce kana actually, instead of just reforming their Kanji usage.
Umm, those Chinese who learn Mandarin do have to learn some form of noun declension and verbal conjugation in order to make any sense of the language, and the lack of an alphabet does not help with that. How would you like to learn, for example, that there are only two tenses - the present and the preterite (no distinct future tense, folks) - and that the sole distinction between those two is aspect, as in the Slavic languages? For non-native speakers of Russian learning how to speak Russian, for example, that bit would be pretty confusing.
Lots of languages do not have articles - definiteness is expressed through other means, such as the demonstratives (in English, that would be the equivalent of using this or that).
Umm, as far as I know Mandarin does use prepositions.
I've alwyas thought that a sort of oposite Japanese system might be fun: root morphemes are written in some kind of alhpabet/syllabary, but there are special symbols for all of the derivational, declensions, and verb conjugation morphemes attached. The interesting thing about doing this would be that even with sound change, since the morphemes are so abstract, they could be kept. Say in English, the plural might be represented with a symbol (I'll assign it <S> for covenience) and then all roots written with it from the unmarked (singular version): i.e. horse v. horseS, cat v. catS. So all the allophones would be unmarked, as can be seen from the previous example; and so would irregulars: goose v gooseS.