It can be applied, although it must be applied cautiously and with some corrections from psychology. I have not been quite just to neoclassical economists, after all. The neoclassicals do not really assume that individuals are absolutely rational. Rather, the neoclassical idea is that on the average, people choose as if they were absolutely rational. The neoclassical economist admits that people make mistakes, but argues that, just because these mistakes are irrational, the mistakes must be unpredictable, and so they will average out.
That's not the whole story, but it is half of it. We have a lot of evidence from studies in psychology, management science, and other fields -- including experimental economics -- that people do make mistakes, and the mistakes are predictable (not unpredictable, as the neoclassical economist assumes) and don't average out. But all is not lost. To the extent that mistakes are predicticable, we can reason back from the choice made to figure out what the rational choice would have been. Suppose, for example, that we know that consumers predictably underestimate the benefits of a burger by 2/9, on the average. When we observe that the consumer is willing to pay $0.90. we can infer that the Economian's actual benefit from that additional machine is $0.90 plus 2/9 of $0.90, or $1.10.
Thus, even though irrational, the choice reveals the subjective benefits. To the extent that the mistakes are predictable, we can correct for them; and to the extent that they are unpredictable, they will average out and we can ignore them. In this way, we can use observations of the choices made in Economia to measure the subjective benefits of production.