A number of people have touched on salient points here.
One to remember is the US-flagged vessels are about as rare as working Yugos. The tax breaks for shipping companies to register in Panama or Liberia or the like just make economic sense. Now, those countries generally prohibit arming vessels under those flags, too, sinc doing so would obligate that nation's Navy to render aid.
Now, the other issue is that many merchant vessels have only minimal crews. 18-20 can be very common, needing only 5-6 per watch to operate the ship. However, a reaction force needs to be trained and available much faster than sleeping off-watches.
Also, the reaction force is going to want more money for being certified and trained and armed up and potentially losing half their sleep. So, you have an additional burden on the merchie owners. To which you get to add 'the fire house' burden--you have to pay for the reaction force every day, every voyage, even when nothing happens. The number of incidents versus uninterrupted voyages is hugely lopsided. But, skimp on your protection, and guess when/where you get hit?
The other real problem is that there can be scads of traffice especially in the coastal transit areas. Tramps, fishers, pleasure craft, all sorts of vessels--and one of those various types is used by the pirates, typically, to get close enough to do the job. Which eats into the potential stand-off distance, and shortens the reaction time for your armed force. Remember, your armed force uh-ohs and fires on a trawler that is not full of pirates, you arein as much trouble as if you let them board you. And, you really can't let them board you--ships are complicated places to defend, and worse to clear.
And, it's not a simple case of we send an O.H. Perry or a Burke frigate along to watch out, either. There are hundreds of vessels out there on all sorts of courses all of the time. Just not enough steaming hours or enough escorts to have much effect. Like the LE radio car nthe beat, the BG would fade away until the coast was clear.
I's hugely complicated. Easy answers are actually few in number. Even the rather simple expedient of finding the next bainbridge and O'Bannion is easy to ask for, but tougher to achieve.