Purpose of Hagalah and Tevilah

Purpose of הגעלה: to cleanse the vessel from actual non-kosher food that was in it לטהרה

Purpose of Tevilah: to prepare the vessel for a Jew’s use after it was available for use for non-Kosher (by a non-Jew) להכשירה

This explains why no tevilah regarding the previous conquered nations, or regarding vessels sold on Pesach, or regarding milk vessels after Matan Torah

במי נדה לא, כג יח ב