That link is about where most teams start their drives. NOT where most teams start their drives after a kickoff which should be closer to the 20 than when you're factoring in punts and turnovers. But let's say the average starting point is the 25 yard line.
To me, each 1st down is 10 yards. 3 first downs translates to 30 yards and that puts a team at their opponent's 45 yard line. That translates to a 60+ yard kick that most teams can't make and won't try. 4 first downs or 40 yards is going to put teams at the normal kicker's outside edge where it's still not a sure thing.
Most coaches, being conservative and not wanting to give someone the ball at the 40+ yard line where they'll only need 2-3 first downs to get into easy field goal range, would punt there unless they have a kicker who's money from distance.
I've seen overtime games where the team wins the coin flip, drives down past the 30 yard line, kicks the field goal to win the game. But I've also seen a lot of overtime games where they were stopped and had to punt.
To me, this everyone "deserves" a possession thing is BS. You only deserve a possession if you can stop the other team. If you're going to go that route, then don't go halfway. Give both teams a possession even if there's a TD scored and then go sudden death after that.