I wrote my masters on using simulated annealing to solve a particular optimisation problem. In a sense, the Gibbs sampler lies at its core, and I really have to agree with you in what you say. At the time I did not have time to think too deeply or too much about it, but I have since really been increasingly awestruck with it, with thermodynamics and statistical mechanics in general, and analogies that can be drawn to all kinds of disciplines.
In bioinformatics, MCMC was used often linkage analysis to sample a "genotype space" of a true inheritance pattern of multiple related individuals to find the location and transmission pathway of disease causing variants.
Classical genetics and statistics were very tightly linked in this regard due to scarcity of data at the time (pre-2000).
Now that the field has exploded with big data, such statistics are no longer so neccesary to answer the same problems, and a lot of the early mathematical elegance associated with the field has given way to brute-force filtering methods.
