Actually, when I was at Midway, there was a hospital - small, but serviceable, with a physician, nursing staff and equiped with even a hyperbaric chamber. A couple of days prior to my arrival, a JA 747 landed with a pax who had suffered a heart attack. Pax got help, operators got money for landing fees, service, Jet-A, etc. etc.

Other currently usable infrastructure at Midway include several cement block two-story buildings (two of them were the "hotel,") a large dining hall, a number of other housing units, a POL tank farm, an air terminal (it could handle a load of pax on the Aloha charter 737-200 ETOPS - yes! - we took there and back.) MOC operated a restaurant that was on the beach of the lagoon, built a la Pan Am Clipper stop.

A significant challenge is that daytime ops can be hazardous when the "gooney birds" (Laysan Albatross) are at Midway, as they cover all areas of the islands; charter ops were always scheduled for night arrival / departure. Imagine a fairly large turkey ingested by an engine, multiply by several...

Of course, all airlines that operate transpacific with ETOPS - covered aircraft would be affected, but AA would seem to be hit fairly hard, with its US - NRT and KIX flights operated with 777s? Maybe CO as well, as I think about it, though CO originates its Micronesia flights at HNL. Those operating 3 or 4-engine aircraft get to skate, AFAIK, though not for medical or other emergencies.