When I was a graduate student - some 25 years ago - there was a practical reason for why Bayesian methods played little or no role in the textbooks. Even though classical methods asked the wrong questions* and forced people to wade through a myriad of complicated and contradictory ways of answering them, it was at least possible to extract point estimates from the data. A practitioner who wanted to address problems more complicated than the linear normal regression model would find that Bayesian methods had very little to offer in the way of concrete advice, so she could be forgiven for concluding that spending time on them was pretty much pointless.
This is a classic example of hysteresis: the persistence of a phenomenon after its cause has been removed. Students who aren't taught Bayesian methods almost never make the effort to learn enough to teach it when they go on to become professors.
Bayesian methods are best adapted to the questions of most interest, and are easier to use. Unfortunately for the next generation of economists - and almost certainly the one after that - this perspective has yet to significantly infiltrate how econometrics is taught.
*Ask yourself which is of more interest:
a) Probability statements about an observed statistic, conditional on an unobservable feature of interest.
b) Probability statements about an unobservable feature of interest, conditional on an observed statistic.
If you answered a), then you are God - or perhaps one of the lesser deities who is bored with just knowing The Truth, and is looking to make some extra cash by betting on what statisticians will conclude from what Nature draws out of its urn of coloured balls. But if your fate is to live among mortals, knowing only what mortals can learn, then b) is the only question that is worth spending time thinking about.