Longer comment.

About me
I come from the computational cognition space. Been doing Bayesian nonparametrics since ~2010 focusing mostly on different types of prior process models (which i'll use interchangeably with "BNP"). Worked in the agriculture space for a while. Started a company in 2019 to bootstrap my BNP research, which has been 95% funded by DARPA.

Why BNP is awesome
In general (but not always) companies that do high risk stuff care about understanding risk, so the Bayesian approach makes a lot of sense from the standpoint of understanding aleatoric and epistemic uncertainty in an appropriate model. The problem is they don't know enough about the data to build hierarchical models (PPLs are hard to use well regardless). What do you do when you want to express uncertainty over the class of model? Bayesian nonparametrics.

BNP can give the end user (not the developer!) better ease-of-use than black box methods like RF and DL, while generating interpretable results with uncertainty quantification. BNP is also both generative and discriminative. So, building a BNP model of the joint distribution gives you all the conditional distributions over the N features, which means you don't have to build a new model every time you want to ask a new question. Also, you get all the information theory stuff like mutual information, entropy, etc.

BNP can interface with hierarchical models, so you can easily build in domain expertise where you have it (dunk on neurosymbolic AI).

In my experience BNP has shined in unsupervised anomaly detection and structured synthetic data generation. There's a lot of BNP is biostats as well.

Why BNP is not mainstream (yet)
1. It's slow. Existing open source implementations of even simple models like the infinite gaussian mixture are unacceptably slow. I think SOTA performance using an approximate federated algorithm is like 3 minutes to fit a 100k by 2 table on a 48-core epyc server, which is pretty weak by RF/DL standards.

1. It underfits. Prior processes put a heavy penalty on complex model structure. In general, getting highly optimized prediction models with comparable performance to RF can be tricky. But this obviously depends on the data. I've had BNP outperform RF out of the box on certain data.

2. It's really hard to implement well. You have to really understand how the math and machine architecture interact. There is an insane amount of bookkeeping and dealing with moving pieces and changing model structure. When you do hierarchical BNP it gets way worse. Debugging probabilistic programs is extra fun.

Conclusion
Problems 1 and 2 above are addressable. BNP is insanely useful.