Why would politicians want to prevent the hysteria that follows a terrorist attack? It harms the country, but it benefits them enormously, allowing them to expand their powers, and boosts their popularity and chances of reelection. The Bush administration, for example, managed to leverage 9/11 into support for the invasion of Iraq, something they had wanted to do since long before, but would have had a hard time selling otherwise. They then rode the wave of hysteria to reelection despite the fact that Iraq had gone fairly disastrously for them.
The government's overreaction was after the populace had freaked out, that is true, but silence can be damning as well. Silence lets hysteria breed. If the President had gone live on national television with a "keep calm and carry on" message, I believe it would have helped a lot. Instead, the government treated it as an existential threat, invoking the NATO charter, declaring a "war on terror", etc. None of this was necessary, and it was all highly damaging, although not to the people in power.
> but it benefits them enormously, allowing them to expand their powers,
yeah, I know, my personal opinion is that Cheney definitely did that; invading a country that had nothing to do with terrorism was evidence of that. I don't see this as Obama's motive though, I think he just wants there to be no terrorist attacks under his watch so that he doesn't sustain more political losses on that front alone (look how much flak he took for benghazi). If there was not such a huge political price for terrorism, I get the impression it would be easier for him to reign in the NSA/FBI. But I can't prove any of this, I'm a dem so I'm biased, etc.
I don't know if I agree with you about Obama, although it's certainly a possibility. Even if we grant that, though, the government isn't one person, and the political losses you mention would come from Congress. The Bush administration had Congress eating out of their hand, but Obama very much does not. And no, sadly, I have no idea how to stop Congress from being a bunch of jerks.
The government's overreaction was after the populace had freaked out, that is true, but silence can be damning as well. Silence lets hysteria breed. If the President had gone live on national television with a "keep calm and carry on" message, I believe it would have helped a lot. Instead, the government treated it as an existential threat, invoking the NATO charter, declaring a "war on terror", etc. None of this was necessary, and it was all highly damaging, although not to the people in power.