Though I cannot know what you might mean by 'perfect chess doctrine', if I make the assumption that my next move should a) loss the least, or b) gain the most, then it's quite possible that taking a piece might be the only move that satisfies that goal. Having agreed on that, it's entirely possible that many further exchanges might present the same choice, ultimately arriving at a board with fewer pieces. As for never ending, that would again have to be the choice of players for the 50 move rules would likely come into play, at which point to keep from ending the game a non-optimal move might have to be made, which might lead to something other than a draw.
Actually, that all sounds way too abstract to me. So, I suggest you just play a wild gambit and hope to outplay your opponent.
I have always thought that chess is very meditative, and, can be seen as a metaphor for existence. I suppose that it could also be stretched to a literal manifestation of the battle at Kurukushetra in the Bhagavad Gita, since there is no reason to want to defeat your opponent, other than that is what the game is, or each players' respective destiny, as it was Arjuna's. What is the perfect chess match? Suppose that two masters of chess played each other, by perfect chess doctrine, would either of them take a single piece? Could the game ever end?