Plastic corks (actually from sparkling wines other than true Champagne, I think) are often hollow with a separate plastic cap, like a little pillbox or something - other than structural integrity, does this serve any purpose?
You mean the metal lid that sits between the wire cage and the top of the soft, spongy wooden cork that, under pressure, could get pushed through the wire cage like jello over time causing the bubbly contents to ejaculate forth upon any convenient surface? Mystery to me too. Republicans must be behind it. 
It does make a handy place to stick a logo that can’t get removed until the contents do.
No; I’m talking about stoppers made from translucent plastic, not cork.
Similar to this one - although this picture doesn’t portray it clearly, the disc-shaped protrusion at the top is often made of opaque white plastic and ‘pops’ off to reveal that the main shaft of the stopper is entirely hollow.
Just off the top of my head I’d guess that:
- It is too hard to mold a hollow “cork”
- The cork needs to be made of soft flexible plastic to properly seal.
- A harder disk on the top prevents the wire cage from digging in.
I love topics like this, I hope there is someone out there from the “Spakling Wine Plastic Stoppers Council”.
“Spakling Wine Plastic Stoppers Council”.
Suitable for covering cracks and filling holes in drywall?
I’ll bet that it’s just easier and less expensive to mold the tops in two pieces.
If I had to guess, I’d say the disk is there to provide a convenient inexpensive way to attach a brand name. Stamping little disks of plastic or metal and then inserting them into a standardized plastic cork sounds to me less expensive than providing custom corks for a variety of customers. Many resellers probably don’t bother adding a name or logo, but some probably do.