The simplest answer to your question of "why is Reuben described using an inanimate entity like water?" is that unlike his brothers who are blessed and likened to various fierce and kingly animals, Reuben is rebuked and criticized for acting impetuously, there is no point in likening him to any animal, since the object is to degrade him for his foolish acts.
However there is something else you need to know (which might change your perspective). I noticed that you accepted the translation of פחז as unstable to be the proper one. Indeed most English translations choose this translation to be the correct one. However, the Jewish commentators translate this word as "rushing" or "hastiness" which in this case (פחז כמים) will read something like: "water-like rushing/hastiness". In other words because Reuben rushed like water to lay with his fathers concubine Bilhah he lost his firstborn rights; his rash imprudent decision is what caused him to lose out. The Stone edition (a Jewish translation) translates similarly, "water-like impetuosity", which is basically the same thing.
The truth his that the word פחז (which is pronounced "pachaz") is not found anywhere else in the bible. The word appears once more in Judges 9:4 (אנשים רקים ופוחזים), but it does not shed any light on its true meaning. Since there are no other words to juxtapose פחז with, the translators translate according to their own understanding based on the context of the verse coupled with common sense. However, Nachmanides a famous Jewish commentator suggests that the closest word to פחז is the Hebrew word חפזון (which is pronounced "chipazon") which sounds very much like it, only the order of the letters "peh" and "chet" are reversed (in English it would be like the similarity between "rebel" and "barrel", though their meaning are wholly different). The word חפזון is found numerous times in the bible and is translated by most as "hasty" or "in haste" (see for example Exodus 12:11). Similarly the word פחז would be translated as "hastiness". Jewish literature (Talmud and Midrash) is also full of references to פחז and they're all found in such a setting. The word פוחזים found in Judges (ibid) can also be translated "impetuous" accordingly; indeed this flows very well with the preceding word "רקים" which means empty, thus rendering: "empty and impetuous people", a euphemism for "bums".
I think that the evidence strongly points to the Jewish translation of פחז as "rushing", "hasty" or "impetuous". This fits very nicely with the context of Reuben acting impetuously to lay with his fathers concubine and thus losing out his birthright.