Well, according to me...
The coolest part of the G.I. Joe mythos created by Hasbro is that the  essential story of the Real American Heroes characters can be lifted up out of  it's original location in history and re-booted into a different time period.  G.I. Joe fans constantly do that, rewriting, re-imagining the G.I. Joe concept  into their own "Joe-verse." 
I think I have finally figured out mine, to somewhat include the 80's  versions and move on into the 10's. This will be a multi-part post, chunks  getting posted here and there.
So on with the show!
"A ruthless terrorist organization determined to rule the world!"
That's the tag-line from the animated series from way back in the 80's -  and it worked back then. Or did it? Did or does Cobra Commander really want to  rule the world? Doesn't he know how much paperwork that would involve? Just the  sheer complexity of the bureaucracy would be overwhelming! So what does Cobra  Commander want?
Again, just my humble opinion...
Cobra Commander is a chaos bringer. He doesn't want to rule the world, he  wants chaos and anarchy. He wants nations to collapse and crumble. He wants  people to come to him for help and guidance and protection.
He will use every means possible to wreak havoc - from open warfare to societal influences. He will latch onto any socially progressive right-wing/left-wing extremist and subvert their cause to his.
He would watch the world burn around him and gather the survivors to his fold.
Cobra Commander is a mad man.
 
