There's not that many that I know of. I do think its much more intuitive and lets you build more nuanced models that are useful for social sciences. You can fit the exact model that you want instead of needing to fit your case in a preexisting box. However, I don't know of too many examples where this is hugely practically important.
The lack of obviously valuable use cases is part of why I stopped being that interested in MCMC, even though I invested a lot in it.
There is one important industrial application of MCMC: hyperparameter sampling in Bayesian optimization (Gaussian Processes + priors for hyper parameters). And the hyperparameter sampling does substantially improve things.