I also wouldn't expect much from giving D3 in a hospital setting since it takes time for D3 supplementation to affect serum levels.

That's why the MATH+ protocol [1] recommends Calcifediol or Cholecalciferol. According to their own review [2] the protocol reduces hospital mortality from 20-30% to about 5%.

[1]: https://covid19criticalcare.com/math-hospital-treatment/pdf-...

[2]: https://covid19criticalcare.com/math-hospital-treatment/scie...