This troubled me greatly, not the thought of going to war and living off the spoils, but that the Chachamim of David HaMelech's time were insistent that the nation could not adequately provide for itself.
One potential answer comes straight out of the Torah, [see: the nerve of some people] where HaShem promises that there will always be poor in the land of Israel. (Devarim 15:11)
But this is the answer I came up with, after a few weeks of thought: (I ran it by Rav Yehoshuah Kohen and he there may be something to it, so I thought I would share it here.)
In David HaMelech's time, we lived according to the natural order, or in Kabbalistic terms, the Achorayim, (hindpart) whereby the world functions more or less according to science in the sense that the system is a closed system and its (essentially) a zero-sum game. In such a setting, as today, growth requires an ever increasing amount of resources and so, naturally, a growing nation cannot suffice to provide for itself.
Later however, in the time of Shlomo HaMelech, once the Beit HaMikdash was standing, this was no longer the case, as the world achieved its more ideal spiritual status of Panim (forepart, or face to face relationship with God) which entirely defies the classical scientific phrasing of the world as a closed system. As long as the Temple stood, the whole world received abundant sustenance from Jerusalem.
There's even perhaps a hint in the words of the Chachamim who made their case before David HaMelech, they said the mouth of a well cannot suffice to fill the well. In other words, rain is gathered from a large area to fill a well, not just the surface area of the well-mouth. This is very much the opposite of the truth in the time of the Temple, when the Temple itself suffices to fill the whole world with blessing.