Having a better defense then offense means we could stop them, start with better field position potentially go into half with small lead. Then get ball at half and extend lead, that’s idea of going defense first. Especially if your defense is your strength.
Take the half out of it and look at a series of a dozen or so alternating possessions between teams. Why does it matter which possessions you stop them on and which you don’t? What matters is how many, and whether they’re getting TDs or FGs. Any order of scoring more than the opponent wins. There are pattern implications: getting behind by too many possessions changes how your offense plays, for example. But if you’ve got a team that gets behind by multiple scores a lot, it doesn’t matter much what you do with the coin toss. But since the possessions alternate, you’re still always trading blows.
In your example above, I get the field position argument. But a bad offense is going to give a good defense filed position to start a half. That can happen in the first half or the second, but again, the effect is the same: at least one starting position where you’re giving up good field position.