Once again this is going to backfire on everyone. And the Pats will be the first to notice and capitalize on it.
I believe statistics have shown that since the current rule went into effect in 2011, the team who gets the ball first has won about 50% of the time. That’s what you would expect and want. Sure, some teams didn’t get a possession, but the overall results are right.
If the rule is changed so that each team is required to have one possession, the team that takes the ball 2nd will win the game significantly higher than 50% of the time (maybe as high as 60%). Why? The team with the ball first will treat it like a normal possession— typically 3 downs to get a first, take the field goal if needed. But the team with the ball 2nd will know exactly what is needed — if the first team didn’t score, they would play it straight; if the first team got a field goal they would use all 4 downs as necessary and adjust the individual play calling on each down as needed (a lot more 3rd down runs and short passes - unpredictability by the offense which favors the offense) but willing to settle for a field goal if needed; if the 1st team gets a TD then it’s the same 4 downs approach without the willingness to accept a field goal. Why would you ever take the ball first?
On top of that, what’s the next logical step? Patriots get ball first and score opening TD, Chiefs/Flavor of the Month come back and get a TD, Patriots come back and hit a field goal. “NOT FAIR! Patriots got to possess the ball twice!!! New rule is that everyone should have the same number of possessions!!!”