Forgive me if I missed something but....

If it was the League of Shadows goal to blow up Gotham City, then why didn't they BLOW UP GOTHAM CITY??????

Once they had the reactor core, they had the ability to blow it up at any moment.

Instead, they chose to inexplicably wait five months for the fuel cells to run down at which point it would blow up anyways.

But they had Batman beat and in a prison far, far away. They had the bomb and the means to detonate it. Bane threatens to detonate it at the football stadium if anyone tries to leave Gotham.

Plus, even if you take that to be a bluff, think about this: when Talia has the knife it Batman's back, after she reveals who she is, knowing that the fuels cells haven't run down yet, she tries to detonate the bomb. This clearly demonstrates that they had the means to eradicate Gotham from the map at anytime in the prior FIVE MONTHS.

So why wait???????? That's never explained.

**EDIT**

Okay, so I know the point was almost explained when Bain said that they wanted to see Bruce watch the city die in despair, and to see his soul suffer as a result.

But they accomplished that a few weeks in. They had a tv in the prison specifically so he could watch the city die. And he did, that's why he threw a rock at the screen and broke it. So mission accomplished right? The city was in despair, and Batman witnessed it. Why no pushy pushy on the button? Kinda stuck out to me.
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"There's a fine line between persistence and foolishness..."
-unknown

"To Each His Reach"
-George Clinton