Surely the Nightingale equivalents are the Javits Centre in New York and similar that have been built across the States.
Comfort’s deployment to New York was to provide a clean facility to release capacity in the city’s hospitals. A role for which she is not designed to do. Comfort and Mercy are basically giant floating trauma surgery facilities.
And the USN were asking for proof that the casualties coming in were covid free. Which pretty much meant they took no casualties.
Comfort and Mercy are designed for Iwo Jima mk2 - opppsed amphibious landings in the Pacific. Like many of the US Military's random capabilities it's a lesson learned in blood, and they're loathe to give them up cf.USAF Combat Controllers - Tier 1/2 SF designed to stop DESERT ONE mk2.