I think you're misunderstanding, there is nothing about using Bayesian analysis that makes you a crank. Using Bayesian analysis where it makes sense is good and sensible and standard practice among just about everybody in the field (although there are some argument about the size an shape of the set where Bayesian analysis makes sense). Cancer treatment would be a perfect example of an area where Bayesian analysis makes sense.
However, for some unknown reason, Bayesian analysis has also become a trendy buzzwords among huge number of crazy internet trolls who seem to think it's a magic formula that can solve all problems, and who have some paranoid delusions that "they" are trying to suppress the knowledge of Bayesian analysis.
On the other hand, there's not a lot of Bayesian analysis taught in high school, statistics 101, or any of the other places that non-stats-nerds are likely to be. It's useful for a lot of things, easy and intuitive (thus its popularity amongst statistical laymen). So why isn't it taught?
The costs of teaching and learning Bayesian Analysis are low (it's just not as hard as, say, the method of moments), and it does have benefits.
My old stats 201 book (Wackerly, Mendenhall and Scheaffer) covers Probability, Discrete Random Variables, Continuous Random Variable, Multivariate Distributions, Functions of RVs, The Central Limit Theorem, Estimation, Properties of Point estimators and Methods of Estimation, Hypothesis Testing, Linear Models / Least Squares, Designing Experiments, Categorical Data, and Nonparametric Statistics. 15 topics (including the introduction), and Bayesian analysis isn't mentioned. Bayes Law is (of course), but only as a theoretical tool, and for solving toy problems about pirates, beads, and rats in the second chapter.
You wouldn't take an engineering analysis book seriously if it didn't mention FEA, but statistics courses can hold their heads up while completely ignoring a useful and easy to teach tool.
Of course, good statisticians and mathematicians will learn about it (later, or on their own), but there's leagues of economists and engineers coming out who will never bother wrapping their heads around it.
Of course, it's entirely possible that it's not so much a conspiracy spearheaded by old-guard frequentists so much as introductory stats courses being focused on teaching a core of theory (LS and MoM), rather then teaching practical tools to people who will use them. You could also accuse introductory math courses of ignoring useful, fun, and easy stuff (scaling?), while focusing on an old, predefined, widely accepted body of theory.
However, for some unknown reason, Bayesian analysis has also become a trendy buzzwords among huge number of crazy internet trolls who seem to think it's a magic formula that can solve all problems, and who have some paranoid delusions that "they" are trying to suppress the knowledge of Bayesian analysis.