The only coin-flip should occur at the very beginning of games. If a team wins the flip and chooses to receive the opening kick-off then, as usual, the other team receives the second half kickoff. If there's an OT then the team that originally received the ball to open the game also receives the "5th Qtr." kickoff. Treating OT like its an entirely different game with its own set of (different) rules is unnecessary. It's still the same game that's being played.
If nothing else, continuing the KO rotation (decided at the game's onset) may cause coaches to rethink their strategy of deferring the opening kickoff. Having the wind at a team's back in the 5th qtr. may also come into play with open-air stadiums. How teams play at the end of regulation could also be affected. I guess it depends upon whether one prefers teams to play to win versus playing for a tie. One is clearly more exciting to me.
Personally, I would welcome having less of those boring play-for-the-tie kneel-downs or three time-eating runs up the gut to close regulation, particularly when it means not having the wind at one's back to open OT. Hopefully, less prevent defense in regulation, too, as teams may be less willing to settle for taking their chances by playing for OT. It would be more exciting to watch more all-out playing to win in regulation instead of playing meekly for the tie.
I'm all in favor of giving teams even less of a reason to take their foot off the pedal, especially late in regulation. K.I.S.S.