Rashi Meilah (13a) and Rashbam Bava Bathra (79a) say that the nisach hamayim must come from מים חיים. The Shittah asks on the Rashbam from the Mishna in Sukkah (48b) which says that the mayim was drawn from the מי השילוח but if it spilled or became uncovered, then the water would be drawn from the kiyor and the opinion of the Chachamim (Zevachim 22b) is that the waters of the kiyor were not מים חיים (see also Rashash in Sukkah)? The Ritva sidesteps this question and he says that the kiyor was mayim chayim for it was filled form the water of the ים של שלמה which was connected to a spring as the Yerushalmi Yoma (19a) notes (see Aruch Lenar.) This also may be the machlokes Rashi and Tosfos if the Gemrah's derash of ושאבתם מים בששון is to tell us that we blow shofar during the drawing of the water or that you need מי השילוח = מים חיים (Aruch Lenar.)
The Gemarah Taanis (2b) מה ניסוך המים מאורתא דאמר מר (במדבר כט, יח) ומנחתם ונסכיהם אפילו בלילה. The Gemarah Yoma (26b) אמר ר' אבא ואיתימא רמי בר חמא ואיתימא ר' יוחנן אין מנסכין מים בחג אלא בתמיד של שחר. On the one hand the nisach hamayim is connected to the tammid of the shachar but on the other hand it can be offered even at night. Rabbi Brown (Mishberay Yam siman 27) wants to suggest that these two derashat are telling us there are two ways of doing nisach hamayim. One way is to offer the nisach as part of the tamid, as a korban and it will have halachot associated with it such as to be offered from מים חיים. However, we learn from the derash that it is kasher at night that even without acting with the rules of korban there is a halacha to bring the mayim as an obligation of the day and for that there is no rule of מים חיים. In other words, לכתחילה the mayim should be offered as a korban but even if that is not fulfilled the Torah still wants there to be a מציאות of a mayim libation but there aren't all the halachot of the "korban" of nisach hamayim attached to it.
Chazal say it was called bais hashoava שמשם שואבין רוח הקודש. There were tremendous heights that one could achieve at the beis hashoava. At the same time, it represents the low waters trying to climb higher. It is even those that are lower down that are able to connect to the beis hashoava. The nisach hamayim had something for everyone to gain.