I know that there is a supplication which says 'protect me from a soul which is never satisfied', so is it okay to supplicate 'give me a soul which is always satisfied', or are we not supposed to always get what we want?

All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.

It is better to recite the reported supplication as it is, and there is no harm in reciting the wording which you asked about. The satisfaction of the soul means that it is content with whatever Allah decrees for it. Seeking refuge from a soul which is never satisfied means seeking refuge with Allah from greediness and the blameworthy pursuit of worldly pleasures.

Al-Qaadhi ‘Iyaadh said, “His words 'a soul which is never satisfied' mean seeking refuge with Allah from covetousness, keenness on attaining worldly pleasures, and having extensive ambitions in this worldly life.”

Allah knows best.