"It is a shame that Bayesian methods are not part of all introductory statistics classes." I don't know if they are now.

I'm a grad student/TA in the statistics department at Iowa State University. Bayes doesn't make it into any of our intro classes outside of maybe introducing Bayes' theorem... but I doubt it. It also doesn't make it into our stat classes for non-major grad students. Some non-stat major grad students take master's level stat courses instead. They introduce some Bayesian material depending on the prof, but not much. There is also a master's level course in Bayesian methods, and new PhD level Bayesian courses in both methods and theory.

Relevant info: our dept. is in the top 10 in the US and so relatively typical, but it is also known for being a bastion of frequentism. Bayesians are making inroads in the department though, but intro classes at Duke, for example, might be much more Bayesian.