1- ancient written chinese appeared as a very specialised language : at first, it was for divination, proclamations of a religious nature, and writings to the ancestor temple (eg the Chunqiu). Those are very different from everyday spoken language. In fact, the first author to put "real world speeches" in the mouth of his characters is Sima Qian (and when he does, the way they speak is quite different from the rest of the text). Also if you look at vocabulary, you can see that many "common" words are missing, or were loaned in ancient chinese. It seems a bit like if written chinese was, at first, quite incomplete and was only extended when it needed to. This does not look like the written version of a spoken language.

2- if ancient chinese was the transcription of one spoken language, the question "which one" begs to be asked. It seems clear to me that there was at least as many different dialects then than now. Yet written chinese (before Qin) seems relatively consistent, no matter where it originates from. This would suggest either there was little different between these spoken languages (strange...), or there was some kind of common language (which one?), or... that written chinese was already different from spoken chinese. Else I don't think Qin could have normalised writing.

3- I doubt ancient written chinese would have been efficient as a spoken language. You can see that nowadays : spoken chinese tends to be more "wordy" than written, litterary, chinese, because without the characters, guessing the words and structures get a bit difficult. Classical is much terser than modern. You can try it yourself: have someone read aloud some passage in classical you never read before, I'm pretty sure you won't be able to guess what it is all about. Actually, even ancient commentators had trouble guessing what some (written) passages meant, you can imagine what it would be without the characters... I don't think such a compact language be useful in everyday situations.

4- This idea of a written language following closely the speech strikes me as a very modern idea. In a world where everyone can read, it seems logical that writing is the transcription of speech. But, again, we're talking of a time when almost no one could write or read, and when only very important things would be written. What then, would have been the point, to be able to write a laundry list, or common day expressions?

My impression (and this would partly answer William's question) is that ancient chinese writing starts as a form of elaborate shorthand, something which helped writing specialised things (divination, then announcements, and sacred songs, which became poems), in a very terse way. As such, it used very simple grammar conventions (ie everything is in the ordering of words, plus a few empty words, but only when it is absolutely necessary: note that empty words are almost always optional in classical, if you can be understood without, don't use them). It also used a very specialised and compact vocabulary (perhaps ancien chinese used two-syllable words too, but written chinese would try to pack everything as one character). Those constructs and vocabulary were certainly linked to some spoken language, but they were not identical to it (a bit like calligraphy does not always accurately represent characters)

As it grew, classical chinese became a game of its own, which tried to pack as much meaning in as little words as possible. You can still find this tendency in modern day litterature.

I would not say that classical is just about grammar. It is a lot about vocabulary, and cultural references. Especially in late classical, the difficulty when reading it is less understanding the grammar (which is relatively simple) than getting all the cultural allusions and prerequisite, ie putting ourselves in the shoes of people who know the classics and the commentaries by heart (whereas most educated people, nowadays, only remember a score of famous quotes from the Lunyu...)