Most people haven't experienced severe side effects from chronic zinc supplementation because they also supplement large doses of magnesium.
Zinc will obviously disrupt the uptake of copper since it has a higher affinity.
Now copper plays a key role in the transportation of

magnesium so when you disrupt the absorption of copper you will inevitably disrupt the absorption of magnesium.
Now the side effects of this can be masked (masked, not fixed) through the supplementation of magnesium and this is why people think that zinc supplementation is safer

than it actually is.
This is also why a lot of people who break out when they take zinc, resolve it really fast by stop taking zinc and using magnesium (other possible causes are candida and a lot of stored iron).

So, zinc is crucial for our well-being, but come on.
Do you really think that pills are better than grass-finished red meat and quality oysters?
You may have to use zinc as a supplement occasionally or in order to battle heavy metal toxicity (in case you ACTUALLY have it), but

you know that foods will always contain more bioavailable nutrients than pills (reason why you notice 30mg of thiamine coming from brewer's yeast wayyyyy more than you notice it from 200-300mg of isolated thiamine).