I still don’t really buy the idea that Qui-Gon would have saved Anakin. I know that was Lucas’ intent, but I don’t buy into it.
There are two reasons why you can see that this would have been the case. First, he is not quite in step with the rest of the order. Anakin needs something extra and this being out of step would have given Qui-gon a different perspective. We see this and Obi-wan even states that if Qui-gon would just conform he’d be on the Jedi Council. But Qui-gon is his own person. The other is that Qui-gon likely would have been more absent from Coruscant and separated Anakin from the influence of Palpatine. I think that when you put those two together that Anakin would have never turned to the dark side. Of course, given that we are talking about a prequel, that wasn’t going to happen. Qui-gon died in TPM for the same reason that Obi-wan did in ANH - drama and story. Adding in that having Qui-gon as master would have changed the outcome makes that story all that deeper. He made Qui-gon the master Anakin needed. And it sheds light on the flaws of the Jedi.