How useful is Bayesian Inference

This may be an unpopular opinion to some, but in my experience Bayesian statistics is not particularly useful in data science in industry, for a couple of reasons:

• A Bayesian approach is very useful when our questions are about statistical inference. However, in data science, more often than not, we are dealing with prediction. There may be some situations where a Bayesian approach works better than a frequentist approach, but I can't think of any off hand, apart from where a conjugate prior is available, in which case we are probably dealing with a very simple model.

• Bayesian statistics usually requires a sampling, such as Markov Chain or Hamiltonian Monte Carlo, and this can be extremely computationally intensive, even for relatively small datasets. In industry we are often dealing with "big data" and a Bayesian model that requires MCMC or HMC just isn't practical.

Edit: To address a comment to this answer:

I have a question about this, how statistical inference is different from prediction. As for my understanding, prediction is usually about getting P(Y=y | X), where X is our data, which is similar with statistical inference

Prediction and inference are completely different. With prediction, all we really care about is the accuracy of the predictions, and that is a relatively easy thing to determine - because the test/validation procedure is minimising some measure of prediction error. On the other hand, with inference, we care about the coefficient estimates and often their standard errors. Often a researcher forms a hypothesis based on a theory of causes - eg, does drinking coffee cause cancer, and they will use a model to determine whether or not the data supports their theory, and to what extent. This is much, much more difficult than prediction. For one thing, in causal inference the basic requrement is that we do not want the estimates for $mathbf{X}$ to be biased - whereas in prediction we don't care if they are biased, provided that we get "good" predictions for $mathbf{y}$, and there are many, many sources of bias in a regression model - bias can and does arise from confounding, mediation, differential selection and colliders. Usually, the crux of the issue is to decide which variables to include in the model in order to eliminate or reduce these biases. With prediction we can use automated variable selection procedure in order to choose which variables to include (feature selection). With inference this is pretty much impossible because automated procedures cannot generally handle the above mentioned biases.

There is a detailed discussion of these issues in my answer to this question:
How Do DAGs Help To Reduce Bias In Causal Inference ?