Picasso’s other strength was his refusal to be absorbed by the ever present academy/salon. They acted as a club, keeping a tight hold on what was and was not considered proper. Picasso could have easily become a part of this, but had the balls to walk away when he was (I think) no more than 16. He went his own way, jointing a studio in Barcelona.
Adding to this was that by the time he was in his early 20s, he had nearly died from illness, and lost a close freind to suicide. This gave his work an emotional back bone it had lacked before. In a sense, it made him.
His most creative move was to take an interest in African masks. Reconciling African sculpture with European painting was impossible. But as every tome on creativity will tell you, new things come from cross breeding old things, all the better if they can’t be interbred.
But whatever Picasso did, he never stopped being a classicist, which is what he had learned when he was a child.
Twombly… I like but with reservation. He died only recently, and has therefore only recently become ‘art history’. He had his thing, and many people liked his thing and would pay good money for it. However, he had none of the scope of some of his peers (eg jasper johns). Certainly, he is far more difficult to use in a classroom unless you are talking about his work. In other words, he is the perfect example of himself (if that makes sence).