Bayesian methods should be preferred as the default.
It's much more constructive (and compelling) to call attention to specific problems with how frequentist methods get used in practice, and talk about how Bayesian methods can help with that problem.
For example, here's Andrew Gelman talking about multiple comparison bias: https://statmodeling.stat.columbia.edu/2016/08/22/bayesian-i...
To transition the next generation of scientists to Bayesian will require universities/stats depts/other depts to do so. Have you seen this to be the case right now? Because in my experience of a few different research settings, almost no one I know, of around 50+ researchers, except those passionate about statistics (very rare person indeed) is using Bayesian methodology.
How to improve Bayesian knowledge in the world? This has its own set of challenges, as Bayesian thinking is arguably more mathematically challenging for most numerophobic people. IMO, it will take multiple generations of effort to transition everyone over.
Many "frequentist" methods can be rephrased as heavily-simplified special cases of the Bayesian approach. Most easily, by assuming a flat prior distribution for the relevant parameters (which is basically an artifact of the parameterization you choose anyway) you can assert that any MLE-based approach will yield a correct Bayesian posterior mode, which in turn is an optimal Bayes-estimator, assuming a constant loss function.
The limits of this whole approach are fairly clear, of course - for one thing, Bayesian stats is generally based on working with the entire posterior distribution, not merely a point estimate of it - and there are good reasons for this. But the basic point stands, and many "tweaks" on the basic frequentist approach can in turn be justified in Bayesian terms. This is not to say that frequentist statistics is all that we'll ever need, but merely pointing out that this whole argument of "we should work with what we have, and focus on making sure that frequentist approaches are put to good use" actually sounds rather vacuous. It's correct in a very limited sense, and hardly something that Bayes proponents are unaware of!
Anecdotally, I can definitely say that the vast majority of American physical scientists I've talked to about this also fell prey to this. With the inverse probability fallacy, one attaches a Bayesian interpretation to P-values, so I don't think training scientists in Bayesian stats would be harder than getting them to use frequentist stats correctly (which is a minefield in comparison).
[0] https://www.researchgate.net/publication/280580018_Interpret...
Do you have any evidence for this? My gut feeling is representativeness is a much bigger problem. Like you do a study on people of the same age race class during the same zeitgeist and then generalize to an eternal law.
The next year fashion has changed and the replication comes out all different.
You know that it's an underestimate because you have prior knowledge about cancer incidence. Bayesian methods let you incorporate that knowledge into estimation process, pulling the estimate up towards a more realistic value.
Undefined variance isn’t nice.
Bayesian treat parameter as a distribution.
The point estimate is base on sample space where as the parameter distribution is base the parameter space.
I think learning both is good and people who pit those two school of statistic against each other are a bit too zealot. They're both tools and use them as needed and when one is easier than the other.