I think this is, at least in part, specific to the US/Western tradition. US physics curriculum is built to get people up to speed with quantum physics ASAP, because this is the core of most physics research in US physics departments. If you look at Landau-Lifshitz's Theoretical Physics curriculum, you will find plenty of classical physics: from fluid dynamics, to elasticity, and plasma physics. For example, Landau-Lifshitz Vol. 6 is an excellent introduction to Navier-Stokes equations and their applications.