Here is one reason to prefer corks:
I was removing the sleeve of a screw-cap, to prepare the bottle for re-cycling. I put the tip of my jack-knife under the edge, carefully aiming the pressure away from any tender part of me. When the sleeve suddenly gave way, my knuckles slid up the sharp edge of the sleeve, leaving me with this.
I almost never injure myself removing a cork.
Now, if the cork industry would just develop an easy, cheap, and infallible test for TCA that could be applied to every single cork just before it was inserted into the bottle, I would be convinced that corks are the perfect closure. Other industries (including the one I retired from) have achieved zero-defect products, why not the cork industry?
At the time we sold the company, we had just gone nearly 5 years without shipping a single defective bolt or screw (billions of them!). The tests required to achieve this are far more difficult to make than testing for the presence of a single chemical compound, and were applied to every single one of those bolts, often at the rate of 8-10 bolts per second.
(BTW, the "defect" from 5 years previously was caused by someone picking up a perfect bolt from the floor, and tossing it into a bin containing similar-looking bolts that had already been tested for defects. We bought back nearly 3 tons of bolts and reinspected them by hand to make up for that error. The one that the customer found - by stopping a semi-automated assembly line - was the only wrong bolt in the entire batch.)