She was the leader of the Avengers for five years after the snap.
Maybe the Russos were trying to resolve it after the fact but it's also possible that they realized during shooting that McFeely/Markus have written nonsense and thus deviated from the script. In my opinion McFeely/Markus are average screenwriters at best and it's known that the Russos changed many things from their script for The Winter Soldier during shooting, so I assume that was the case in later movies, too. I even read somewhere that the time travel rules were different in the original Endgame script and were changed by the Russos. So McFeely/Markus obviously wanted to go with the Back To The Future approach and didn't really get what the Russos went for in the finished movie, which would explain their clueless statements.
Also director's word trumps writer's word as the director is the one who decides how the finished movie looks like, at least as long as the studio bosses or producers don't interfere.
It was always the plan for him to come back to his timeline, therefore he had a second particle that he used to travel back. He should bring the stones to their timelines and then return, that's why Hulk, Sam, and Bucky were puzzled that the platform stayed empty as they were expecting him to come back, so it's clear he had a particle to return with.
Here's what could have happened without the scene being a plothole: He lived his life with Peggy in the other timeline, then used his second particle as an old man to return but didn't navigate to the point directly after he left but maybe 30 minutes prior, so he came back on the platform before Hulk and the others were there and went to the bench to sit down waiting for Bucky to spot him.