i think i’ve said this before and i’ll say it again - i see Qui-Gon as the perfect jedi, and i’m pretty sure Anakin saw him as the perfect jedi too. and i think that that’s very important to the overall saga.

Qui-Gon was the jedi Anakin really looked up to and wanted to be like, while other jedi in the PT such as Obi-Wan and Windu represented a lot of what was wrong with the order (a factor that ultimately ended up pushing Anakin over to the dark side). i also think that, during RotS, Anakin lost the notion of what was right and wrong (obviously) and ended up painting jedi and sith with the same brush - meaning that in his head both groups were equally bad - and so he chose to join the faction that could save his wife and didn’t condemn passion. and i think that, in the end, Qui-Gon was the only jedi he ever saw as a truly good man.

with that in mind, i think that RotJ Luke is a very similar character to Qui-Gon in TPM in terms of how they act and their moral standards. i think Vader saw that too, and that seeing it made him see hope in the jedi once again, since the only living jedi was, then, as good a man as Qui-Gon, the man he looked up to his whole life. and i think that was one of the main factors that made him save Luke (besides Luke being his son, the most important factor imo), which ultimately means that from my understanding Qui-Gon is a very important character overall.