At the end of the day, what do you do with Bayesian Estimates? I have often heard that in certain instances, it can be more beneficial to use Bayesian based methods because they provide "a distribution of possible answers" (i.e. the posterior distribution) instead of a single answer (as done in the frequentist case). However, it seems that at the end of the day, the analyst is still required to transform this "distribution of possible answers" into a single answer.
For example : if a Bayesian model is used to estimate the posterior distribution of "mu", the analyst is still required to either take the MAP or the Expectation of this distribution to return a final answer.
Is this the main benefit of Bayesian models? If the priors are correctly specified, the credible intervals associated with the expectation of the posterior distribution (of the parameter of interest) are more reliable?

I can't give a de jure benefit of Bayesianism, but I can offer some examples of how I find Bayesianism beneficial as compared to frequentism.
That the results of a Bayesian analysis is a posterior distribution and not a point estimate allows the analyst to perform some very straightforward calculations in order to perform decision analysis. As I explain here, the posterior can be used to estimate the expected loss of any decision (assuming a cost function is specified) simply by taking averages of samples obtained via MCMC techniques. This assumes one has a good model readily available (perhaps a benefit, perhaps a detriment depending on where you stand) but I can't underscore just how simple the calculations can be.
From some of the points you make in your post, it sounds like you're caught on the fact that people still want a single number (the expectation of the posterior, for example, or the MAP of the parameters).  The sample mean implies a particular cost function (the sample mean for example minimizes the sum of squared errors).  But, if you wanted some other cost structure, then with Bayesianism you're free to use an estimator which caters to your needs, as I do in the link above.
