I agree that a benefit of Bayesian analysis is flexibility. Different posterior results are possible with different priors. But in practice this can be a hindrance as well as a benefit. When answer depend on a choice of prior, misusing, or misunderstanding the prior can lead to incorrect conclusions.

There is also a very attractive feature of Frequentist guarantees specifically for A/B testing. They make statements on the long-run average lift, which is a quantity that many businesses care about: what will my average lift be if I implement a variation after my A/B test?

That said, we have, and continue to look at Bayesian methods because we don’t feel that we have to be in either a Frequentist or Bayesian framework, but rather use the tools that are best suited to answer the sorts of statistical questions our customers encounter.

Finally, there have been some very interesting results lately on the connections between sequential testing and bandits! (for example, see here: http://auduno.github.io/SeGLiR/documentation/reference.html )

Could you state clearly what this guarantee is? Unless I'm making a stupid mistake, such guarantees are impossible even in principle with frequentist statistics.

This is not a theoretical problem. I have a client who wasted months on this.

I know how to fix this (a Bayesian method, BTW), but I haven't published it. As far as I know, there is very little published research into using Bayesian bandits in assorted real world cases like this.