After the Vikings-Saints NFC Championship game (and the Colts' failed attempt to go 16-0) the argument for this change to the rules is even more compelling. If this rule had been implemented, both the Saints and the Colts would have still had something to play for in the last month of the season.
To summarize, we have two major problems:
1) The coin-flip winner has an unfair advantage in overtime.
2) Teams like the 13-0 Saints and 14-0 Colts have no incentive to win after they have clinched the top playoff spot (making any of these late-season games utterly unwatchable).
The solution is elegantly simple: automatically award the "coin flip" to the home team.
In addition to eliminating the coin flip, there are a number of other positive effects:
1) This increases the importance of home field advantage in the playoffs.
If a team like the Colts go 14-2, they get an edge if a playoff game goes to overtime (just as the home team in baseball has a strategic advantage).
2) We now know who the "home team" is in the Super Bowl. And it matters.
This would have been pivotal this season: the Colts and Saints would continue to play hard, knowing that if they met in the Super Bowl, home-field advantage would be determined by their regular-season record. Instead, we got five unwatchable games by two teams that had nothing to play for.
3) It adds drama to the final minutes of a game, and clarifies strategy for coaches.
If you're the away team, and you're up against a good offense, you want to play for the win, not the tie, in any last-minute play calls. You go for two if you have the chance. And you go for the touchdown instead of the field goal on 4th down. More excitement, and less overtime (which tends to run into the next game, which doesn't make most football fans happy).
4) It increases attendance.
As the NFL becomes more fun to watch on TV, ticket sales are suffering. Giving the home team a bigger advantage increases the likelihood that a home-team fan will have a great experience at the stadium (by getting to see his or her team win).