Porque como Himarm menciona acima, eles não poderiam ser escravizados através dos anéis, e de fato (do ponto de vista de Sauron) os únicos efeitos que eles tiveram sobre os anões foram positivos:
For the Dwarves had proved untameable by this means. The only power over them that the Rings wielded was to inflame their hearts with a greed of gold and precious things, so that if they lacked them all other good things seemed profitless, and they were filled with wrath and desire for vengeance on all who deprived them. But they were made from their beginning of a kind to resist most steadfastly any domination. Though they could be slain or broken, they could not be reduced to shadows enslaved to another will; and for the same reason their lives were not affected by any Ring, to live either longer or shorter because of it. All the more did Sauron hate the possessors and desire to dispossess them.
De Senhor dos Anéis , Apêndice A, parte III: "Durin's Folk", ênfase minha.