Money doesn't just buy people.
You'd essentially be drafting them.
In every country (except maybe Iceland which doesn't have a standing army), the military has plenty of medically trained soldiers who are used to doing these things away from home for months
Seems far more reasonable than locking down entire countries for months, asking people to forego friends and family (without even mentioning the consequent unemployment).
You wouldn't need to force anyone with a gun. A five-fold increase in wages - untaxed - would be more than enough incentive. The cost would be a drop in the ocean compared to the damage wrought by the measures adopted so far.
No need to use a gun. Just a strict contract.
Care workers have to go in and out of elderly care facilities. We still don't have much data on how good COVID-19 testing at tracking pre-symptomatic cases, but the data points at "certainly not 100% accurate".
Even if you tested _every_ care worker before they entered the building, you'd likely miss some asymptomatic cases who could go on to transmit to the elderly. Nevermind the fact that earlier in the pandemic, the kinds of near-instant tests we have now (allbet with unimpressive reliability) weren't available.