There is a YouTube channel called Ask Sebby. This channel has a video everyday about maximizing travel and cash back through credit card points. Today's video was about ... the Green Card (and I immediately thought of this thread).
The takeaway was, let's say in the past you signed up for other AMEX charge cards (Gold, PRG, Platinum) and for whatever reason you don't have them anymore (doesn't make sense to pay the AF, etc.). You can get the Green Card and wait until you have an AMEX offer to upgrade to one of the products you've already owned for X amount of points. This would be a way of double dipping on sign up bonuses for the same product which wouldn't normally be available if you just signed up for the card again due to AMEX's once in a lifetime rule.
I'm not a chunner so I never think of these things. Pretty interesting though.