You guys are thinking too small.
POD the US Navy fobs off hospital ships to USCG. Lightly/zero armed USCG hospital ships are allowed to sail inside waters of hostile countries. USCG hospital ships help during numerous mass-casualty disasters. When they need serious airlift, USCG borrows CH-53 helicopter squadrons from USN and USMC. Anything smaller than CH-53 just clutters the flight deck.
POD North Korea - sort of - explodes a dirty nuclear bomb over Guam (or any of a thousand island nations) causing massive numbers of patients suffering from radiation sickness. USCG helicopter carriers/hospital ships rush to the rescue.
Alternately - to circumvent long- term financing problems - USCG requisitions a small container ship from the merchant marine. She loads a bunch of specialized containers for a one-month exercise. Specialized containers contain: X-Ray machines, surgical operating rooms, blood banks, pharmacies, jet fuel tanks, helicopter work-shops, close in weapons systems, depth charges, torpedoes, etc. The top layer of containers is reinforced to allow CH-53 helicopters to land.
Container load varies with the mission.
Arctic and Antarctic missions sail on ice-reinforced container ships. Early exercises only last a month or two, but USCG light carriers prove so popular that they soon sail 11 months out of the year.
As for anti-pirate duties off he coast of Somalia ....NATO, India, China, etc. have all sent frigates. Chasing pirates with frigates is like waaaaaaay overkill ...... like swatting mosquitos with a sledge-hammer! The job would be better done by slower ships carrying lots of helicopters. 20 cannon are enough to sink any Somali pirate vessel.
The days of commercial vessels hiring private military contractors as guards is so passé. Retired NATO special forces operators proved too expensive. Now the work goes to the lowest bidder who hires any Baluchis, etc. idling in Third World ports. When neighbouring nations feared heavily-armed PMCs staging coups, they shifted guards to Arsenal ships that stay in international waters.
In conclusion: The anti-piracy role is far better served by medium-sized helicopter carriers with at least a dozen birds on deck.
Retired Master Coporal Rob Warner, airframe technician who sailed aboard HMCS Iroquois and HMCS Athabaskan. I have hot-refuelled hundreds of Sea King helicopters at night, in heavy seas, etc.