Fine, so there are flaws in the study.
I am no researcher but from what I have read, why don't they take the thousands of people coming into hospitals testing positive each day, enroll them into the study, separate them by what appears to be the most common biases (age, sex, even body mass index and skin color), give 1/3 placebo, 1/3 vitamin D3, 1/3 leave alone as control group. A couple of months later measure the results and publish.
Sounds doable to me, specially in such a large scale crisis. Since there is little financial incentive for big pharma to test this, again, why are governments ignoring these strong hints?