Are Bayesian Inferences Weak for Wasserman's Example?

An example was given in the textbook All of Statistics (Wasserman, 2004, pages 186-188) for arguing that, in the problems with a great many parameters Bayesian inferences are weak, because they rely heavily on the likelihood function that captures information of only a tiny fraction of the total parameters. Alternatively he suggested non-Bayesian Horwitz-Thompson estimator, which cannot be obtained from a likelihood-based approaches, including Bayesian approaches. He argued that Horwitz-Thompson estimator is good since it is unbiased and consistent. In this paper, I compared the mean square errors of Horwitz-Thompson estimator with a Bayes estimator at a wide range of parameter configurations. I also simulated these two estimators to visualize them directly. From these comparisons, I conclude that the simple Bayes estimator works better than Horwitz-Thompson estimator for most parameter configurations. Hence Bayesian inferences are not weak for this example.