Corks are on spirits products because the consumer has a perception that cork = quality. That is a poor way to judge a product. Corks are archaic 19th century forms of sealing bottles and they are not as effective as more modern methods.
BT experimented extensively with synthetic corks a couple of years ago and found none back then that they thought were satisfactory. With lower proof wines the synthetics seem to work just fine but not so with higher proof alcohols. The synthetic tends to taint the product as the alcohol breaks down the plastics.
Natural cork, no matter how good it is, and BT uses the best available from Portugal, will have some level of failure, usually a taint from natural molds in the cork, even though they are treated to get rid of this. Also corks will dry out and stick to the bottle if not kept wet. Eventually a cork will break in the bottle if stored a long while.
The wine industry would dearly love to get rid of corks because it would reduce considerable losses they experience from cork taint.
No doubt about it; a screw top is best for your wines and your bourbons in the long run. But every distiller and vintner is afraid of breaking the "expectations" of consumers. Some wineries are getting braver on this but we have a long way to go before corks are gone.
So, if your bourbon has a cork, drink up before it dries out. Now, that isn't such a bad solution, is it?