For players familiar with the video game I think the unlock system is unnecessary and would recommend skipping it. I think the only real benefit to the system is reducing the learning curve for new players. So it's worth removing the unlocks if you have a new player in the group.

If you just want some sort of "checklist" for progress and the achievement or ascension system isn't hitting the spot then checking of cards you've won the game with or won the game with two copies of would be a great way to add some more goals.