If the number of combinations of sounds in your language's sound system is lower than the number of things and actions you want to talk about, words might have to get pretty long to unambiguously represent ideas. To avoid having to talk so much, we might use shorter words that would be ambiguous without context. I think this is kind of what's going on with spoken Mandarin. Too few sounds are chasing too many ideas, so there are necessarily a bunch of homophones. But it still works fine, as long as there's context, and the listener can ask for clarification.
But reading a book isn't a dialogue. The reader can't ask for clarification. Maybe this is part of the reason Mandarin tends to be written differently than it's spoken? I'm not sure, because I'm not advanced enough. Reading advanced Mandarin like in newspapers is very daunting. In text messages and IMs, my friends and I seem to write exactly how we'd talk out loud, and it works fine. But maybe this is because we're talking about simple subjects?
There are actually at least two issues here. One, Mandarin written with Chinese characters is often written differently than would be spoken aloud. Two, reading Mandarin in pinyin would be annoying.
On the first issue, I think it may be possible to write Mandarin just like you'd say it -- I think maybe it's just a tradition to make it so stilted. On the second issue, I think the problem is that there would be a bunch of annoying misparses that required back and forth clarification.
What do you mean by "information density of a language"? The way you used it makes it sound like a human language must have a certain "information density" to be useful, and that in English this is achieved via complex grammar but in Mandarin it is achieved via complex characters.
That is confusing to me, because if a certain level of information density is necessary for an effective human language, then wouldn't it be necessary to have that in both the spoken form and the written form of that language?
With most languages, the written form and the spoken form are essentially the same language. Any sentence in one can be expressed in the other. People often use longer sentences and more complex sentences when writing, and use more redundancy when speaking, but that is due to the medium, not the language being expressed using that medium--with the written language the reader can control the rate of reading and can jump around in a sentence if needed to deal with complexity, so longer and more complex sentences work better written than spoken. They are still the same language. One could write just like one speaks, or speak just like one writes. Is this not the case with Mandarin?