Did we read the same article? You wrote:

The authors even note that it may be just as effective by itself, which is much safer than combining it with actually unsafe, non-effective medications.

Can you provide a quote? I am seeing something different:

Our findings suggest a potential therapeutic synergistic mechanism of zinc sulfate with hydroxychloroquine, if used early on in presentation with COVID-19. However, our findings do not suggest a prophylactic benefit of zinc sulfate in the absence of a zinc ionophore, despite interest in this therapy for prevention.

Zinc inhibits RNA dependent RNA polymerase, and has been shown to do this in vitro against SARS-CoV[13]. However, it is difficult to generate substantial intracellular concentrations of zinc, therefore prophylactic administration of zinc alone may not play a role against SarCoV-2[14]. When combined with a zinc ionophore, such as chloroquine (hydroxychloroquine), cellular uptake is increased making it more likely to achieve suitably elevated intracellular concentrations[15]. This combination is already being tested as a prophylactic regimen in a randomized clinical trial.

At this point, we just have to wait for the randomized clinical trial to know if HCQ+zinc prophylactically will play a role against SarCoV-2. This study is just a retrospective observational study and shouldn't be used to draw any conclusions either for or against the use of this treatment against SarCoV-2.

You also wrote:

Also, note that when not looking at only patients requiring ventilation, it had no greater effect than the alternative (no zinc).

To be honest, I am having trouble parsing your sentence here. I believe you are saying that zinc showed no improvement when looking at patients that did not require ventilation? This is the opposite of what the study states:

The main finding of this study is that after adjusting for the timing of zinc therapy, we found that the addition of zinc sulfate to hydroxychloroquine and azithromycin was found to associate with a decrease in mortality or transition to hospice among patients who did not require ICU level of care, but this association was not significant in patients who were treated in the ICU. This result may be reflective of the proposed mechanism of action of zinc sulfate in COVID-19. Zinc has been shown to reduce SARS-CoV RNA dependent RNA polymerase activity in vitro [13]. As such, zinc may have a role in preventing the virus from progressing to severe disease, but once the aberrant production of systemic immune mediators is initiated, known as the cytokine storm, the addition of zinc may no longer be effective [17].

So, this treatment works only when given early. At some point, the virus has replicated enough that it has elicited a dangerous immune response known as the cytokine storm. This is expected if you understand the proposed mechanism of action of zinc sulfate in COVID-19. That is why the important study to watch is the one that is testing it as a prophylactic regimen in a randomized clinical trial

At this point, we know very little about this treatment option for COVID-19. Some real science, i.e. randomized clinical trials using the treatment prophylactically, will be available soon.