1. A team was already assigned to take out Nagato. Didn't take long at all. Maybe 15 minutes.By that time Pein would've left with Naruto. And most of the survivors were in no condition to fight.
Thousands of injured and tired shinobis.
Not most but many.
2. A team was already assigned. That means not 100% of Konoha was injured as you foolishly believe. In fact, they even had multiple shinobi stay back in Konoha to taek care of the injured, one of which was Hinata. So you can thank that bravery for keeping even more Shinobi from helping.
3. You've completely disregarded individual motivations and actions in favor of this bias. From every perspective in the manga, Hinata's actions were foolish and a waste. Did they succeed due to plot? Yes. Were they the right thing to do? Absolutely not.
I'm not sure how many different reasons you're going to try to give here, but none of them are going to stick.