I think the initial narrative will be a hodgepodge of different things but centered around 2 major themes:
1. The greatness of LeBron: how he brought a championship to Cleveland, 3 rings, and revisiting 2015. It's clear now he would have won in 2015 if not for the Irving and Love injuries, and he still took the Warriors to 6 games by himself last year.
2. One of the greatest seasons ever, filled with records, upsets, and the unpredictable which shows the diversity/balance in the league. We had 2 teams challenging for 70 wins, with 1 setting the all time record, yet neither won the championship. Only 9 teams ever came back when down 3-1 before these playoffs, now we have 2 more in back-to-back series. No team has ever come back 3-1 to win, then lose the next series when up 3-1, blah, blah, blah.
Not that I necessarily agree or disagree with 1 or 2, but I can just picture all the ABC and ESPN analysts talking about those things now following a Cleveland victory in Game 7.
As for Green and Bogut, I don't think they're big enough stars to be part of the narrative. Even if they were, the narrative is rarely centered around the losers. In '11 I think the narrative was more about Dirk, Cuban, and Co. rather than the superstar-laden Heat not delivering a championship. Only hardcore C's fans think the loss in 2010 was because of Perk's injury. Nobody really cares that Karl Malone was injured in '04 or how the Lakers were imploding, everybody just talks about the Pistons victory and their team defense. In '05 the narrative wasn't Sheed not guarding Horry on the inbounds play, it was more how great Duncan and friends were, back where they belong. Sure there will be some talk around some of the many what-ifs by hardcore fans and some talking heads as they try to fill up a 1/2 hour or an hour tv show or podcast, but the main narrative will be on LeBron's greatness and how awesome the NBA is in general and how any team can win.
historically you are correct, you remember the winners not the losers, but initially there is a lot of talk on the losers especially if it is an upset, shock, etc.
Sure, I think there's more talk initially of the losers and all the what-ifs, but that's only because you have these 30, 60, 90 minute programs that have to talk about something. The majority of the talk immediately following championships still focuses on the winners though.
The majority of the post game coverage will focus on the LeBron and the Cavs, the next day the the leading segment on SportsCenter and the front page of USA Today and every website that covers sports will have a story front and center about LeBron and the Cavs, a week later LeBron will be on the cover of Sports Illustrated, etc. I'm sure there will be other articles and coverage on the Warriors, and the talking heads will debate about 73, Curry, Green, etc. but that's not what's going to drive the narrative, it will be more of a side story.