Dejounte Murray could reach his first plateau
The final spot on this list very nearly went to Luka Samanic, but because fans have seen so little of him on the court playing meaningful minutes, I think it would be a mistake to go into the season with many bold expectations for him. While he certainly looks like he's done his due diligence in the weight room, only time and playing time will tell whether or not the Spurs have something with him.
When considering the remaining players' roles on the team and their potential to improve, Dejounte Murray strikes me as the player that could end up falling short of expectations. While the same could potentially be said for Jakob Poeltl, I don't think he has the potential to become a franchise-changing talent as Murray does, and I find it doubtful that many have sky-high expectations for him (particularly on offense).
Murray, on the other hand, has primed fans to expect the most from him. Despite tearing his ACL early on in his career, since then, he's significantly improved in virtually every offensive metric and has remained very consistent on defense. He has more or less become the face of the Spurs and is now the longest-tenured member of the team with Patty Mills gone.
With that in mind, it should go without saying that many fans will be coming into the season with very high expectations of him. In terms of both scoring and playmaking, DeMar DeRozan will be leaving a gaping hole in the Spurs' offense now that he signed with the Chicago Bulls. Fans will likely be primarily looking to Murray to fill that void in the starting lineup, and he may or may not be able to make it happen.
The biggest hole in Murray's game on offense at this point is by far his three-point shooting and, while I don't necessarily expect him to take more threes, I do hope and expect for him to become more efficient with them. If he can even become a league-average three-point shooter, I think it will tremendously open up the other parts of his game on offense.
Ultimately, I still have quite a bit of hope for all of White, Walker, and Murray, but they will have high expectations going into the 2021-2022 season. After two missed playoff appearances in a row, seeing improvements in each of them will be key in determining whether or not they will be a part of the Spurs' long-term plans.