There are other benefits to Bayesian data analysis besides being able to handle limited data. There are problems with the outputs of frequentist analysis around the quantification of uncertainty. For instance, from simulation studies we know that the aleatoric coverage probability for confidence intervals of a selected confidence level varies depending on the size of the difference in plausibility between the null and alternative hypotheses. And a given confidence interval says nothing about epistemic uncertainty for this particular experiment. This can make the outputs of frequentist analysis difficult for stakeholders to utilize, whereas Bayesian epistemic probabilities are generally more easily understand by stakeholders, and can directly feed quantitative decision analysis methods.
An interesting book on adapting frequentist methods to create confidence distributions that can better express uncertainty and can optionally incorporate prior information using likelihood functions is this: https://www.cambridge.org/core/books/confidence-likelihood-p...
A good introduction to some additional problems with frequentist methods vs Bayesian and likelihoodist methods is this: https://gandenberger.org/2014/08/26/intro-to-statistical-met...
An interesting book on adapting frequentist methods to create confidence distributions that can better express uncertainty and can optionally incorporate prior information using likelihood functions is this: https://www.cambridge.org/core/books/confidence-likelihood-p...