Class Participant YML suggests that maybe taking the wealth would have make the Jews wealthier than Haman, raising Achashverosh’s paranoia.
The Sfas Emes notes that the three incidents in which the verses emphasize that the Jews did not take the spoils parallel the three actions of Shaul and his people for which the threatened annihilation of the Jews of Persia served as a tikkun – the sparing of Agag, the sparing of the livestock, and the taking of the Amalekite gold and silver.
The Ginzei HaMelech writes that although the Jews did not take the spoils, the verse implies that someone did; namely, Mordechai. Mordechai did, indeed, take the spoils by accepting Haman’s house (Esther 8:2). He used this wealth to help finance the rebuilding of the Temple. In a powerful display of vinahafoch Hu (“and He reversed”), Haman’s wealth was used to build the very structure which he dedicated his life to destroy.