That's an interesting idea that might have worked. It looks to me like they're modeling the story's timeline on the humans and then compressing the elvish timelines to human-length.
It would have been a challenge to keep the flashback approach from getting really confusing, and there are several plot threads that need to weave together. I'm guessing it would be deemed too risky.
On the third hand (I have a lot of hands), the timelines of elves and Men don't really need to come together much until Elendil and Isildur are already alive. Another approach might have been to just explicitly indicate that the threads are moving at different speeds in time. In my head, that's essentially how I'm viewing it. You might even be able to frame that approach as an extended flashback to go with your idea, with some elf who survives (Elrond?) sitting around by a hearth somewhere, explaining events leading up to the present.
The plot thread with Galadriel and our deposed Southlander king would be more difficult that way.