There aren't enough warships to escort every merchant ship that passes through the area, which is well over a million square miles of water. The pirates usually don't make their intentions known until they are in close proximity of their target. They don't fly the skull and cross bones like in the days of old. Positioning of warships s a matter of luck. A small boat (45 kts) can easily outrun a destroyer (35kts.). Visibility on a clear day at sea is about 15 miles in all directions under ideal conditions. Radar cannot identify if a ship is a pirate ship or not, too many small fishing boats, etc. But small radar sets can determine cargo ships (big blip, slow speeds). Pirates have the advantage, unless they are within visual sight of the warship and identified as such. Also it would be impossible to stop and check every small boat for weapons. Compare it to X # of police (representing the number of warships available) (this would be less than 100 if all navy's sent some ships)assigned to count the Y#  of people in Manhattan everyday (representing ships and small boats). This is what it would be like.

I'm with you though, if a few were sunk the rest might look for a different line of work.