You're absolutely correct that Bayesian approaches are not magical and do not suddenly supply you with vastly more information than frequentist approaches (particularly when you have a really poor prior, in which case the Bayesian approach will be similarly poor). Bayesian statistics is certainly very popular right now, but it should not be looked at as some sort of panacea for all statistical problems.
However, I would say that Bayesian approaches do have a big advantage in terms of helping with the interpretation problems that plague frequentist significance testing. Namely, as the OP article points out, Bayesian approaches reformulate the testing question in a way that is more intuitive, i.e. "what is the probability of the hypothesis given both the prior probability and the new data?". So yes, Bayesian methods surely do not fix everything, but since interpretation of statistics is such a major concern, they can be quite beneficial.
However, I would say that Bayesian approaches do have a big advantage in terms of helping with the interpretation problems that plague frequentist significance testing. Namely, as the OP article points out, Bayesian approaches reformulate the testing question in a way that is more intuitive, i.e. "what is the probability of the hypothesis given both the prior probability and the new data?". So yes, Bayesian methods surely do not fix everything, but since interpretation of statistics is such a major concern, they can be quite beneficial.