My guess: Zinc isn't patentable, nobody can make money from selling it so nobody will do research to see if it works.
While that might be what's driving it there are ways around it. Zinc isn't directly patentable but you could patent a specific way to package it.
I could imagine packing it in Lozenges with copper might be a good idea. Taking a lot of Zinc reduces your copper absorption, so that you need to consume more copper when taking a lot of Zinc. It's also possible that the copper helps directly.
But wouldn't governments have a big incentive to do this? Even for private companies, it can bring them a lot of goodwill for presumably not that much money ...
There was significant interest in zinc early on. It seemed like one of the most promising avenues for protecting oneself against Covid-19. Searching on both Google and Lesswrong itself, I do not see new research on it. (This is the closest thing I found; A metareview that says there is almost no research whatsoever.) Its epistemic status seems frozen in the pre-Covid past: promising experimental treatment with no significant evidence confirming or disconfirming it, and no largescale commercialization and deployment.
This seems quite an inefficient result, if my understanding is correct. What has gone wrong?