Sudden death overtime only makes sense in sports in which scoring is inherently rare and anemic, like soccer.
For football, especially in the playoffs, there should be no sudden death. Even the worse teams in the NFL are going to score 14-20 points most games. And in the playoffs, those bad offensive teams won’t generally be there. It doesn’t take much to score a FG. No sudden death. No first touchdown wins. Just add another timed extra period and play until 0:00. Don’t want to make it a full 15, fine. Make it 10 minutes. But sudden death doesn’t make sense in a sport where scoring is not rare or difficult.