Problems with huntin' pirates:
1. Gub'mints don't approve other folks usin' force. They like to think of themselves as sole legitimate users of force. Otherwise, freighters and cruise ships headed for "iffy" locations would have a decent armament for self-defense and insurance companies would reward 'em for it.
2. Pirates have nothin' worth taking and nobody is payin' for their extermination.
#1 might be a bit of a problem, i admit. However, what if if you make a paying business out of pirate-hunting? Like safaris, where adventurous people with scads of cash could pay for the privelege of shooting up a bunch of lousy stinking cutthroats- and of course, sign a waiver against their being injured or killed in the process.
The gov't can tax the activity, and rid themselves of a nuisance at little or no cost.
See? Free enterprise at work!
Of course- to quote a line from "The Wild Geese",
"My God! The UN will go mad!"
I can dream........