I was going to say the same thing. The requirements for having a “win” in overtime have been met at that point and the game is over.
It’s the same reason why teams currently don’t kick an extra point in overtime; for now, a touchdown in overtime wins the game regardless of anything else, so the game is already over before any extra points can be attempted.
Can’t do that, legally. As long as the ball is live, play must continue.
Certainly, Team A should take a knee or go down or out of bounds as soon as they gain possession, but the officials cannot blow the play dead until the play is over.
ETA: As an example from the college ranks, which, I know, is not quite the same: this season, the game between Kansas and West Virginia went into overtime. Kansas scored a TD and XP on its initial possession. Then, on its first possession, West Virginia threw an interception. The Kansas cornerback who intercepted the pass returned it 80+ yards for a TD. Once he gained possession of the ball, the officials did not blow the whistle, but let the play continue to its conclusion.
If the first team to possess the ball scores a field goal or touchdown, after which the second team loses possession by an interception or fumble, the down will be permitted to run to its conclusion, and all rules of the game will be enforced as customary, including awarding points scored by either team during the down. Only fouls that require the down to be replayed, fouls that negate a score, or palpably unfair acts will be enforced.
So if Team B fumbles, Team A regains possession, but then Team A fumbles and team B recovers and scores, team B gets those points for their score. But if the play ends without a score, the game is over.
And the new rules add some interesting strategy. Say both defenses are completely gassed, as is the usual case when you go into overtime, and the offenses are pretty much moving at will. Team A scores a touchdown, kicks the PAT, are now up by 7. Team B scores a touchdown, and are now down by 1. Do they kick for 1 point, thereby giving the ball back to Team A who now only need to get into field goal range to win? Or do they go for 2, and win or lose the game right there?
I went to a Monday Night game at Arrowhead years ago. It was an ideal evening, with no wind. When we crested the hill overlooking the stadium, the parking lots were covered with a haze of smoke. It was quite the experience.