I have spent a lot of time trying to use PPLs (including Pyro, Edward, numpyro, etc.) in Real World data science use cases, and many times mixing probabilistic programming (which in these contexts means Bayesian inference on graphical models) and deep networks (lots of parameters) doesn't work simply because you don't have very strong priors. There are cases where these are considered very effective (e.g. medicine, econometrics, etc.) but I haven't worked in those areas.

NUTS-based approaches like Stan (and numpyro) have more usage, and I think Prophet is a good example of a generalizable (if limited) tool built on top of PPLs.

Pyro is a very impressive system, as is numpyro, which I think is the successor since Uber AI disbanded (it's much faster).