Isn't consistency simply another word for intellectual integrity? The fact that actions are inconsistent may be due to the imperfection of the actors. The internal contradictions may also be the work of opportunistic individuals, seeking their own advantage.
But the following examples suggests that inconsistency can indeed be a value:
in nature and in social interactions, in law, and even in science. Compromises are often only to be had if each side breaches its principles. Laws often join incommensurable elements; otherwise no agreement would be made between the interest groups. Then, at best, adjudication can subsequently bring about consistency. Those familiar with the fundamental relativity of normative arguments must allow parallel, but mutually exclusive arguments for the very same finding. Coherent conceptions are long-term cultural achievements. It is thus imprudent to repudiate a conception if it is falsified in reference merely to a single matter. The more complex an object of research, the sooner even the science studying it will have to accept internal inconsistency. One interpretation of quantum mechanics has even had more unsettling effects. It was only possible to explain things here once it was accepted that nature itself is inconsistent.