Why isn't a polar protic solvent used in the Finkelstein reaction?

Usually, in a nucleophilic substitution reaction, a stronger nucleophile replaces a weaker nucleophile.

In any polar protic solvent, the order of nucleophilicity is $\ce{F-}<\ce{Cl-}<\ce{Br-}<\ce{I-}$ (due to stronger solvation of the smaller anions).

While in any polar aprotic solvent, the order of nucleophilicity is $\ce{F-}>\ce{Cl-}>\ce{Br-}>\ce{I-}$.

Why does the Finkelstein reaction use acetone in spite of the fact that it is a polar aprotic solvent? Wouldn't using a polar protic solvent be better since it would make $\ce{I-}$ the strongest nucleophile of the group.

$$\ce{R-X + Na+ ({acet.}) + I- ({acet.}) -> R-I + NaX v}\tag{1}$$