Browsing through the research area of the top 100 US News statistics program, almost all of them are heavy in Bayesian statistics. However, if I go to lower tier school, most of them are still doing classical/frequentist statistics research. For example, my current school (ranked between 150 to 200 on QS world ranking for stats so not considered a top tier school) has only one professor focusing on Bayesian stats and there is almost a resentment towards Bayesian stats. Some grad students I talked to even says that Bayesian Statisticians are doing Bayesian stats for the sake of it which I of course disagree strongly.
However, I wonder why this is the case. I'm having several educated guesses:
(a) there is not enough room left for advancements in the methodology of classical/frequenting stats and the only viable research in classical/frequentist stats research is on applications which will be the main focus of lower tier school as top tier school should be more inclined towards theoretical and methodological research.
(b) It is heavily field dependent. Certain branch of stats is simply more suitable for Bayesian stats such as many scientific application of stats method while other branch is more suitable for classical stats such as financial area. (correct me if I'm wrong) Given this, it seems to me that top tier schools have a lot of stats faculties doing applications in scientific field while lower tier schools stats department are mainly focusing applications in financial area since that helps them generate income and funding.
(c) There are huge problems with frequentist method that can't be resolved for example the prone to overfitting of MLE, etc. And Bayesian seems to provide a brilliant solutions.
(d) Computational power is here hence Bayesian computation is no longer a bottleneck as it was 30 years ago.
(e) This one may be the most opinionated guess I have. There is a resistance from classical/frequentist Statistician that just don't like a new wave of methodology that can potentially overtake the role of classical stats. But like Larry Wasserman said, it depends on what we are trying to do and everyone should keep an open mind, especially as a researcher.