What interests me nowadays is how seriously this was taken by intelligent people. My sophomore-year undergraduate art history course cast a deterministic process for Western art where the ultimate, end-of-history was abstract art as currently practiced by highly publicized New York City painters. I'm pretty sure our instructor, a senior staffer at the university's art museum, was largely influenced by Clement Greenberg (1909-1994).
The Greenberg Wikipedia link just cited has a sub-link to something called medium specificity, a fancy term for picture plane honoring that I hadn't been aware of.
Tom Wolfe in his often-hilarious way dealt with the business of flatness and abstraction in his 1975 book "The Painted Word." In it, he features the influence of important New York art critics, including Greenberg.
Here is a taste of Greenberg's writing from "The Role of Nature on Modern Painting," Partisan Review, January 1949. He was discussing the rise and importance of Cubism, but the passage below includes some of his thinking regarding flatness.
"By dint of their efforts to discover pictorially the structure of objects, of bodies, in nature, Picasso and Braque had come -- almost abruptly, it would seem -- to a new realization of, and a new respect for, the nature of the picture plane itself as a material object; and they came to the further realization that only by transposing the internal logic by which objects are organized in nature could aesthetic form be given to the irreducible flatness which defined the picture plane in its inviolable quality as a material object. This flatness became the final, all-powerful premise of the art of painting, and the experience of nature could be transposed into it only by analogy, not by imitative reproduction. Thus the painter abandoned his interest in the concrete appearance, for example, of a glass and tried instead to approximate by analogy the way in which nature had married the straight contours that defined the glass vertically to the curved ones that defined it laterally. Nature no longer offered appearances to imitate, but principles to parallel."
This is sophistry. Its premise and conclusion are that flat painting surfaces are determinative.
They are not. Great artists can and do whatever suits them on those innocent flat surfaces. They can paint flat color areas, they can create illusions of three-dimensionality, they can even go the collage route by pasting foreign objects on the canvas or board. Greenberg and his followers were placing art in a straightjacket through use of an arbitrary premise from which constrictive deductions were made.
Let's look at some examples.
Greenberg was a huge Pollock fan, yet here was Pollock painting actual layers of colors atop a flat canvas.
Mondrian, on the other hand, for many years painted very flat, not-curving images using only black, white and the three primary colors. Can't get more basic than that.
One-point perspective began appearing in Western painting in the early 1400s. "One point" refers to a single vanishing point, found here between the two figures framed by the most distant arch. Artists in Raphael's time were thrilled at this means of showing depth on a flat surface. Eventually, two-point and three-point perspectives were discovered.
Another way to portray distance is called "atmospheric perspective" which involves the greying-out of increasingly distant objects caused by particulate matter in the air.
Here Waterhouse uses both linear (mostly regarding the boat) and atmospheric perspective.
The background pedestal has linear perspective. The figures are given three-dimensionality by use of light and shade to suggest their surface modeling.
Manet's paintings often had a flatter look, though the small figures reflected in the mirror behind the barmaid diminish in size with distance, just as Raphael's did in "Athens."
Cézanne attempted to reconcile depicting a 3-D world on a 2-D canvas with crude, though influential, results.
Feininger was influenced by Cubism, but only superficially. Note the one-point perspective and the atmospherics in this painting.
An impressive, comparatively recent painting making zero use of Greenberg's ideas.