This critique might come from the idea that having a good analytic model, or at least some valuable analytic insights, involves much more than assigning some priors. Of course, the two things don't exclude each other, but for some frequentists Bayesians have the wrong perspective - or at least that's the critique, whether it's true or not.
Another issue that I personally have with Bayesianism is that I believe that assigning probabilities to singular events is only meaningful and admissible at all if there is a good analytic explanation for the respective propensity. For example, we may be able to deduce that a die is reasonably fair from the way it is constructed and our knowledge of physics, and later confirm this by frequentist analysis. Merely believing or claiming that the die is fair is not acceptable. Again, the difference is only one of attitude in the end, I suppose.
Maybe philosophers have given Bayesian statistics a bad rap, too, because many of those who call themselves Bayesians are also "probabilists", i.e., they think that rational belief must conform to the probability calculus. There are many arguments against probabilism and the only arguments that speak for it are Dutch book arguments. The view does not have very strong foundations.