We still think about supply and demand, but we also think about policy, psychology, behavioral genetics, and much more.
Some random comments:
I wrote about Masonomics as thinking about incentives, signaling, institutions, and evolution. I have heard Nobel Laureate Douglass North complain that he did not want to call what he does "institutional economics," because he sees it as broader social science. Nobel Laureate Robert Solow once warned economists against doing "amateur sociology," but in the context of a paper in which he admittedly was doing so in order to explain wage stickiness, which in turn was necessary to explain unemployment. George Akerlof, another Nobel Laureate, delves deeply into sociology. In 2005, the Journal of Economic Perspectives published an article on economic sociology.
What are the problems with sticking to the traditional paradigm?
1. To explain a society's transition from poverty to prosperity, you need to invoke institutions.
2. The traditional paradigm has this strange dichotomy, in which market behavior is rational and self-interested but policymaker behavior is perfectly altruistic. These idealized constructs are very limiting. Note that the Left tends to complain about the limitations of the rational model of the market actor, while the Right tends to complain about the altruistic model of the policymaker.
3. The attempts to do macroeconomics based on rational actors and incentives seem strained and unhelpful.
4. As Nobel Laureate Robert Fogel points out, in the developed world we are dedicating a smaller share of resources to producing food, clothing, and shelter (including durable goods). The growing sectors of the economy are health care, education, and leisure. The production of food, clothing, and shelter can be well described by using traditional factors of production--labor, land, and capital. Not so with health, educational attainment, and the enjoyment of leisure, where psychological and social factors are important.