Oh really?! As a learner I also thought that "please do" was polite.
Though for some reasons I always use "could you please...". Anyway, I agree that any language have ambiguous expressions. It is probably natural to give an ambiguous reply, when the direct one is somehow risky for a speaker. And surely it also depends on a person and their style of language. Then don't you think, that the Japanese are more often in such risky situations than Europeans, Americans?
On the other hand, Japanese ambiguity seems to be inherent into the structure of the language. I meen ellipsis, passive tense. I feel, the Japanese use them much more frequently than Russians (my mother tongue sometimes becomes redundant, so a listren has a clear idea of "who, when, where, what and what for") or the English. Another thing is homonimy, that can also provoke misunderstanding.
So I personally have divided ambiguity into two: this objective one, that has to do with grammar and lexics, and subjective one, that, as Mike Cash said, is a kind of social agreements. And that if, from my point of view, is a personal perception of the language, and hence can't be proved. But I wonder, why it has become so popular?! I have never read anything about English or Italian ambiguity, whereas you will find a lot of works (both in Japanese and foreign languages) dedicated to it. Why has it become so important? Or exaggerated?