But note also that the Church teaches:
The satisfaction that we make for our sins, however, is not so much ours as though it were not done through Jesus Christ. We who can do nothing ourselves, as if just by ourselves, can do all things with the cooperation of "him who strengthens" us. Thus man has nothing of which to boast, but all our boasting is in Christ . . . in whom we make satisfaction by bringing forth "fruits that befit repentance." These fruits have their efficacy from him, by him they are offered to the Father, and through him they are accepted by the Father. (CCC1460 quoting from the Council of Trent)
If we do not do this we are still due some punishment. The Catholic Church calls this "temporal punishment".
But I don't want to make too much of this. The main purpose of Purgatory is purification. It's what the term comes from
Purgatory
“early 13c., from M.L. purgatorium (St. Bernard, early 12c.), from L.L., "means of cleansing," prop. neut. of purgatorius (adj.) "purging, cleansing," from L. purgare (see purge).”
(Online Etymology Dictionary).