If there’s one thing this nation is good at (particularly referencing our military), it’s logistics. We have the ability to supply massive fighting forces at pretty much any location around the world including pop-up ICU’s, surgical suites, etc. Putting that to work domestically would alleviate the strain on civilian services if the need arose.
As fate and coincidence would have it, I'm the officer-in-charge of one of those mobile surgical suites right now, in Italy. (A role 2 FRSS/STP for those who know what that is. We were here before any of this COVID-19 stuff started, completely different mission. We are not caring for any COVID-19 patients at this time.)
Couple issues -
1) We're supplied and equipped for trauma, not ongoing ICU care. And just initial resuscitation and damage control surgery at that, not comprehensive trauma care. Our holding time is limited by personnel, equipment, and consumable supplies - measured in hours, perhaps a day. But not weeks. We also have a substantial non-medical logistic tail that is rather cumbersome and inefficient if viewed in terms of cost/resources per unit of deliverable medical care.
2) An even larger issue is that just because COVID-19 is rearing its ugly head, doesn't mean our mission supporting warfighters goes away. Crises beget more crises, and the sort of world events that require people with guns to handle (with a FRSS/STP supporting them) are more likely now than they were three months ago. The military mission we're supporting isn't going to go away and free us up.
3) When the military deploys one of these things, they haul the roughly 40,000 pounds of tents and generators and all the other gear out of a warehouse where all the stuff is stockpiled ... but they haul the people (doctors, nurses, and techs) out of hospitals. At this point most of us anticipate that hospitals everywhere are likely to be overwhelmed, so it's probably best to leave the people there. Pull some vents out of a warehouse, convert some ward beds to ICU beds.
Our role here in Italy, should the actual brick & mortar hospital here be overwhelmed with COVID-19 patients, won't be to pop up our 4 tents and establish another facility. We'll just go to the hospital and work there. We have about a dozen portable ventilators but I'm not sure they're up to the task of being ICU vents keeping ARDS patients alive for a week or more. In theory we could convert some ward rooms to ICU beds but it's not like we brought along a fleet of ancillary services. We have an xray tech and a lab tech, and very limited lab capabilities and supplies (think transfusion and ER-level trauma labs). These patients require far more resources than just a ventilator.
If this was a geographically confined crisis, it would possibly make sense for the military to pull physicians, nurses, and other persons from military hospitals and send them to that region. We see this all the time for natural disasters. The tsunami, Haiti earthquake, hurricanes in the southeast USA. At the moment however, every US military hospital in the world is making plans to best manage an overwhelming number of patients at their own facilities. Shuffling people around and setting up tents may not be helpful in the big picture.