Do we have some evidence to back that up?
Conclusion: This study provides the first in vivo evidence that zinc sulfate in combination with hydroxychloroquine may play a role in therapeutic management for COVID-19.
This one is underway: https://clinicaltrials.gov/ct2/show/record/NCT04377646
That's great but that doesn't exactly tell us that hydroxychloroquine + zinc is better than other therapies or even better than nothing.
The clinical trial is regarding the efficacy as a prophylaxis for a small portion of the population that is most directly exposed. It would be great if it works but it will likely not be as useful as a treatment as we can't necessarily give our whole population a years worth without seeing other health consequences.