I would expect much of the pattern would be related to prosody. In this context, prosody would refer to the natural "chunking" or partitioning of Mandarin. That is, Mandarin seems to have a tendency to "chunk" into pairs of syllables.
For example, I would expect the answer to the question "你有没有钱？" to be "我没有钱", "没钱", or "没有" rather than "没有钱", "我没钱", "没". It is not that the latter are necessarily grammatically incorrect, but they are not as typical/don't quite sound right.
This is also related to the "rule" (not a strict rule, it seems) that a single syllable noun takes it's adjective with a 的 if the adjective is bisyllabic and without 的 if the adjective is one syllable. For example, "绿色的球" and "绿球", rather than "绿色球" or "绿的球".
I think this tendency is also related to the reason why so many Mandarin words are two syllables. It also relates to how to break up a series of third ones for tone sandhi; many of the lexical chunks tend to be two syllables (see this answer, for example).
The above "rules" are by no means strict. Also, I am not a native speaker and so welcome any corrections to my examples. I also welcome any suggestions for sources, as I forget where I first saw this bi-syllabic tendency.