Wine writers tend to mention only two types of closures: natural corks and screwcaps. Plastic "corks" make up about 20% of the market -- twice as much as screwcaps -- but we tend to ignore them.
This is a mistake on all of our parts. There are good arguments to be made for natural cork, and good arguments for screwcaps.
There's really no reason whatsoever to use a plastic closure. They're inferior in every way.
Plastic "corks" let in oxygen at a far higher rate than natural cork, and of course much higher than screwcaps, for which oxygen entry is still an issue. The air entry increases over time, so that if a wine with a plastic cork sits around for 2 years, it probably has already started to oxidize. Thus you should look carefully at the closures on wines in the discount bin or at Trader Joe's.
There are two reasons wineries choose plastic over natural cork: price, and the absence of TCA, the cause of "cork taint" that can spoil a wine.
The cork industry has eliminated reason 1 by producing cheap corks made up from amalgamated cork particles. Industry reps say these are actually less likely to have TCA than more expensive corks because they have more surface area to treat. Without consulting an independent scientist, I can't say whether that's true or not. But they are price-competitive with plastic.
As for reason 2, fear of TCA is a legitimate reason to switch from cork. But why switch to plastic, which you know is going to lead to oxidized wines? That's just trading one flaw for another. If you really fear TCA, use screwcaps.
I admit that I'm ignoring the market reality that many older Americans think there's no romance in opening a bottle with a screwcap. Let me tell you, there's no romance in breaking your corkscrew on a plastic cork, as I have done more than once.
I'm not sure why nobody writes about plastic closures. Most of the big U.S. wine companies use them: Constellation, Gallo, the Wine Group, Jackson Family Estates. Consumers need to tell them that we don't want plastic.