I wrote in my parent comment that this was based on personal observation. There is no such thing as conventional wisdom on such topics, there are just widespread opinions:
Note, there are two points we are discussing here:
1. Is there a way of saying that some grammar is more complex that others - objectively?
2. Does writing influence the complexity of the grammar?
Now, for both cases, I base my opinion of observation, and not off any scientific papers. Since you are doing the same, the only way we can settle this duel is by trying to show as many examples one way or the other to resolve the issues.
Regarding the first question, I'll just assume that we both accept that there is difference in complexity in grammar between languages. Or do you not think so?
Regarding the second question, I'll say this:
* Chinese Grammar is simple, but it's very clear that Chinese style writing cannot have the same influence. If you do not know a chinese word, you cannot write it, and you cannot read it. As such, you are not likely to use it, and the word will tend to die. In western style writing, you can attempt to write a word from having heard it once. It's also much easier for words to live on, because words are easily copied.
* Unwritten Creole and Pidgin Languages always do very similar things to western languages - they strip it of certain grammatical constructs, and it ends up being like most unwritten languages - past tense and future tense are created by adding words, and not by changing words.