That's oversimplified and encourages the behavior IMO. At least a partial solution would come in the form of port seizures and continued interdiction from a multi-national naval team.
Well its highly doubtful the pirates are launching out of ports. You can launch a dhow from any ragged swamp. Next you couldn't compare a port operation as a "seizure". It would more be like an invasion and your'd better have 10,000 marines along, along with, an awful lot of firepower. And for what? All those new casualties and picture of dead Somalian kids? Also the USN has always been much more concerned about the safety of ships under the American flag. And why shouldn't we be? Think the Russians, Saudis, Turks, Japs, or Chinese would give a damn about us?
Mostly this is all small freighter stuff. We Yanks don't really do that kind of business and any Yank seaman has better sense then to sign on with a small freighter operating out of those waters with an American passport.
I say dial up the United Nations. Let those pimps and prostitutes deal with it, "in between lunches at high line NY restaurants with their Diplo plates parked everywhere".