It’s interesting that you criticize Qui-Gon’s death and bearing on the story, when Lucas ultimately managed to better flesh out Qui-Gon’s character, motivations, and relationships with Obi-Wan, and Anakin over the course of a single movie than Snoke was developed over the course of two movies in the ST. I would say Snoke is to Ben Solo what Qui-Gon is to Obi-Wan and to a lesser degree Anakin, only Snoke has far less scenes, and Snoke and Ben Solo’s relationship is far less developed obscuring Ben Solo’s character motivations.
Let’s try not to get too far off topic with the ST talk, especially when the comparison is so labored and irrelevant to the discussion.
The problem is Qui-Gon is basically the closest thing to a main character in TPM, and then he’s gone. There are two things that went wrong - he should have been far more in the background in a mentor role, and his influence on Obi-wan and Anakin should have been more clearly conveyed in the other films (which is to say more than not at all, which is the case).
Anyway, I’m going to give this as half a point in favor of ROTS.
I used the example to point out a possible double standard, but I might have used ANH as an example as well. Tarkin serves as one of the main antagonists in that film, and after ANH he’s gone, never to be mentioned again. However, Tarkin serves a purpose beyond his apparent role as the villain. Firstly, ANH is far more political than TESB and ROTJ. For one the political situation is mentioned or discussed on numerous occasions, between Leia and Vader early on, in the Death Star conference room, and again between Tarkin and Leia before the destruction of Alderaan. The more personal story of Luke, Obi-Wan, and Vader is very much in the background, and used as a McGuffin to get Luke to join the fight against the Empire. Secondly, Tarkin and Vader are exponents of two different worlds, the old and the new. Tarkin’s presence is a constant reminder that Vader is a leftover of a bygone era in a world where technology is seen as the ultimate political tool. With Tarkin’s death Vader comes into his own, and the personal story of Luke, Vader, and Obi-Wan is put front and center in the next movie.
Qui-Gon’s character serves a number of purposes. For one he is the mirror that exposes the Jedi order’s dogmatism, a dogmatism that would continue to plague them in subsequent films. Secondly, without Qui-Gon’s involvement Anakin would never have been trained. Qui-Gon’s actions in the story directly impact the further development of the main characters, and the development and outcome of Lucas’ six part story. Thirdly, Qui-Gon’s death is a stark reminder to the Jedi order that the Sith are still at large and as dangerous as ever. The death of a main character reminds us of the stakes, and also conveys the idea that Anakin has lost a father figure who might have steered him on the path of the righteous. That void is filled by Palpatine who would take over the role of father figure in subsequent films to the detriment of the entire galaxy.