Shelley develops Frankenstein through the frame structure (a story within a story) to allow the reader to get several characters' perspectives. By the end of the novel, three characters (Walton, Victor, and the Monster) have had a part in the narration. Perhaps Shelley thought that it would be too confusing to the reader to keep switching narrators outright.
The frame structure also works well because Shelley builds suspense from the beginning. By being able to view Victor first after his pursuit of the Monster, the reader wants to know what has made Victor so sick, why he was pursuing a creature, and what brought him to such a remote location. By using Walton as the overall narrator to whom the story is told, Shelley can easily begin with the suspenseful "present" and flash back to the causes of Victor's condition.
Victor Frankenstein and Walton are mirror characters. Walton longs so badly for knowledge and recognition for his scientific experiments/discoveries, but Victor knows the danger of an obsession with science and knowledge. He has one last opportunity to dissuade Walton from becoming like him. If he can save another from enduring what he has had to endure, then perhaps not all that he has lost will be in vain.
I think you could also consider how this makes the entire impossible story a bit more plausible. Walton and Victor are both explorers, pushing the bounds of knowledge and science into places where it might best not go, and becoming isolated from those that love them. Walton's letters, and interesting device in themselves, present something that we believe could be "real." If we buy into the reality of Walton, it becomes a little easier to buy into the strange story of Victor. And if we can buy into Victor's strange tale, when we arrive at the onion's core, the Creature's story, we might just be a little more likely to buy into it. And then we exit the core through the Victor layer and back out to Walton level and "reality." It's and interesting device and I think it works well!