Here’s the problem.
The team that gets the ball first actually has a disadvantage of being deep in their territory, assuming there’s not a big kick-off return.
So a turnover or a three-and-out, pretty much gives a huge advantage to the other team, since they’ll have much better field position, plus they know all they have to do to win is to kick a field goal.
That’s why historically it’s been about 50-50 in terms of the team that wins the coin toss winning in Overtime.
Don’t have a kickoff. Have each team start at a particular yard line, like in college. In college you start at the other team’s 20 yard line. Maybe in the NFL, it would be maybe the other team’s’ 40 yard line. Something like that.