Shipbucket

While they are probably better armed, they are also completely untrained and standing in a dinghy that's dancing around in the middle of a big ocean and they have zero cover. So far they have never come close to hitting a helo due to their aforementioned ability to stay out of assault rifle range. And unlike the helo in New Orleans the Helo crew knows exactly where the bad guys are and that they are likely to return fire. And they are cleared to return said fire.
Again operational experience proves you wrong. With almost no exceptions the pirates have always retreated when a helicopter has shown up, unless they are far enough along with the attack that they've started shooting and/or throwing grapples etc. In those situation the helicopter is allowed to open fire.

Except it didn't stop them. In Asia it didn't have any real effect, they avoided European targets because they had an annoying tendency to carry and godawful amount of guns. In later times it has had more to do with strategy. Since Asian pirates tend to sell everything including the ships themselves, attacking a big containership, or anything else that isn't a small coaster for that matter, would be pointless since they wouldn't have a clue about what to do with it.
Again experience doesn't agree with you. There has been reports of attacks as far east as Sri Lanka.

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Source Materiel is always welcome.

I've been looking into the issue over the last few days... I can't find a single incident of an aircraft sinking a pirate vessel, and I cannot find an incident where a helicopter was used.

All other captures of a pirate vessel or one that the pirates had captured involved a warship actually doming alongside and ended in an old-fashioned "away all borders" scenario, after which the pirates were either dead or in handcuffs.

Most of the situations end in a ransom- costing not only a massive ransom, but the loss of revenue and cargo related to the ships capture and delays. This is hardly the way to be handling the pirates- when one pays the Danegeld, one seldom rids himself of the Dane. All ransoming is doing is reenforcing the success and profitability of piracy.