At this point the vaccines aren't doing much if anything to stop transmission, so I don't think there's much of a basis for mandating the vaccines to control the spread. I'm sympathetic to the argument that the unvaccinated are more likely to burden the healthcare system, but I think mandates on that basis are a dangerous precedent that could enable the government to try to control all sorts of things that burden the healthcare system. In any event, reducing the burden on hospitals is well outside the purview of OSHA (or the DMV or DOT for that matter).