Reading this discussion, everyone seems to assume that there are only two alternatives: natural cork and screw-cap. But there is a third one, a foamed rubber made to look and behave like natural cork. This should combine the the aesthetics of the old way and the reliability of the modern way to bottle liquids. There might be one draw-back, it might be much more expensive than natural cork.
It is a misconception that cork should let air into a bottle. Exactly this should not happen. To make sure, some bottles are sealed with wax or something similar on top of the cork. Synthetic materials are much safer in this respect.
The problem in using a synthetic material is the time that wine is in a bottle. Many liquids are bottled nowadays with screw-caps. The sealing is due to a thin layer of an elastomer. Usually these liquids stay only weeks or months in the bottle. Wine might be much longer in contact with the seal, 30 years or more, and it contains alcohol, a solvent for some additives used in polymers. Nobody knows what will happen in such a long time. There is no reliable way of predicting the aging process. I heard rumours that there are bottles lying in the many cellars with synthetic seals, and the change of wine and seal is monitored. But obviously, these experiments started only several years back. We will have to wait for many more years, before the grand red wines will be sealed with synthetic seals. And I'm very confident, that the use of natural cork will end when a good replacement is found.