We can't be certain that the spirits are destroyed. Though it seems highly likely that is what Obsidian intended for us to believe. And for that I can credit your position.
However, the choices in Mask of the Betrayer with regards to the soul eater mechanic need an understanding of the character's situation in order to appreciate. It is not truly a choice for the character to devour a soul. He has to. The devouring of souls becomes, to him, a highly natural state. The sole exception to this is with, as you can see in reading the description for supress, a remarkable excercise of willpower.
It is simple for us, as players, to see it as a choice and devouring the spirit as malicious. But, judging by what is presented in narratives and descriptions as the game, it's not so easy for the character. It's not as easy as choosing between two abilities. He's supposed to devour as an almost natural state. We only ever hear of one other Soul Eater who just lays down and dies. We never hear of one other who suppresses it. And despite how "malicious" the act supposedly is, there is not a single character in the game who condemns the PC for it outside of the few times he expresses it as a concious choice (in dialogues). This all fits in with the description for suppress that seems to regard to act of suppressing as almost supernaturally difficult (and how useless it is for non-Okku companion PCs who have significant craving), despite how easy it is for a player to just press the button.
Maybe Obsidian could have presented this more clearly.