I would say it depends on the application. Sometimes biases are large with strong negative impacts on the resulting impact assessment (could be large errors in precipitation that will deteriorate results in a hydrological model). In such cases bias correction can be highly beneficial - given that high quality observational data are there. In other cases it may be that errors are smaller and it is more important to have an internal consistency among all different variables (which is not the case with bias correction that is most often done for one variable at the time).