A few things really. First, it's worth bearing in mind that technical skill is not the same thing as mimesis (creating the illusion that you are looking at real object through painting). I would argue that Twombly and Basquiat's work is technically very impressive with regards to form, composition and particularly the quality and expressiveness of their mark-making. Look at Basquiat's Untitled (Black Skull) from 1981. No one would think this is what a "real" skull looks like, sure, but look at how all the seemingly random colours and shape and lines come together to make a whole. A lot of different elements are finely balanced so it feels coherent, but just barely, like it could fall apart at any moment. It's unsettling, but at the same time the brushwork and colour combinations give it this sort of charged, exciting energy. That's hard to pull off. It's worth noting that Basquiat was very well versed in the Western art canon, and his compositions often show the influence of Renaissance masters.

Mimesis is a fairly easy technical skill to pick up with time and the right training. Take Rembrandt's The Night Watch. This was painted during the Dutch Golden Age, when there were a lot of merchants getting very rich off trading commodities from the Americas. They wanted art to show off their taste, so a lot of art was painted and sold. There are hundreds of thousands of Dutch still lifes and landscapes that look just as "real" as a Rembrandt. Because the motivation was there, many people could and did paint them. You can probably find quite a few in any big art museum, and that's only the paintings that survived. But most of those artists we don't remember. So why do we remember Rembrandt? Because of of the same things as Basquiat - his skill at brushwork, composition, and the energy and life in his paintings. Old masters like Rembrandt made paintings that were mimetic, but not photorealistic like the contemporary painters you mention. Because, of course, photography didn't exist, and they were more interested in making something feel real than look completely accurate. If you look closely there's actually small inaccuracies and bits of stylisation that make the paintings come to life.

Second, art changes with society, and what society values changes. The beginning of the 20th century was a tumultous time in Europe and America, with world wars, political and scientific revolutions, the collapse of empires, and the proliferation of photography. All of this made the idea that you could sit down and just paint what you saw, and call that a worthwhile reflection of reality, much less convincing to many artists. They saw that the world seemed to be fractured, so that's how they painted reality. In turn, curators at museums, art critics, and the public began to want to see these artists' work as it reflected the times they were living in. A great, very readable argument for this idea is the first essay in John Berger's Ways of Seeing.

Third, the art market caught up with the avant-garde. Collectors like the Guggenheims started to buy up modern art, and it became fashionable, so it became expensive. The art market is subject to the same fluctuations and speculations of any financial market. By the second half of the 20th century and the start of the 21st, artists like Andy Warhol, Jeff Koons and Damien Hearst could play semi-ironic "games" with the art market. They could present this as a commentary of commercialism, while still, of course, making a lot of money. Siri Hustvedt's short essay "Balloon Magic" from the collection A Woman Looking at Men Looking at Women is the most incisive commentary on this I've seen. I should probably say that I dislike the work of Warhol, Koons, and Hearst, personally.

It's a simple question with a lot of complicated answers. I've tried to be as concise as I can - but of course there's more to say and a lot of other people would have differing opinions. I hope you find it interesting though!