A century ago, many wines were not fit to drink – either damaged by heat in shipping or bacterial spoilage. Worse, the wine market was awash in fakes, bottles with fancy labels that looked like the real deal, but that contained cheap wine or even tea. In those days, inspecting the cork could provide actionable information, indicating which bottles had been improperly stored, for example, or betraying the true provenance of those that were fraudulent. But since these problems have long since been eradicated, the ritual presentation of the cork has outlived its usefulness.
When corks are presented tableside, guests often instinctively inspect them or sniff them – not because they know what they’re looking for, but because they don’t know what else to do. There’s not much we can learn from the cork anymore, though, and it will inevitably smell more like cork than like wine, so it’s better to just ignore it and wait to sniff the wine instead, once it’s poured. If the wine smells and tastes appetizing, great. If it smells like a mildewed basement after a flood, send it back and ask for a fresh bottle.
In short, if you’re collecting corks or making a corkboard, by all means, grab your cork when it’s presented and put it in your pocket. If you’re buying the bottle, the stopper is already yours. But, if not, there’s no need to fiddle with the cork at all. Just leave it on the table. Wine corks are trash–like clam shells or olive pits–so someone will eventually clear it out of your way.