Assuming I'm a marketer who's using A/B testing tools and who's only interested in getting "statistically significant" results, and assuming Bayesian methods provide some advantage in terms of regret minimization that translates to real dollars earned, I feel that I could totally outsource my understanding of the theoretical underpinnings that get me that result. After all, what percentage of Optimizely or VWO users perfectly understands the statistical framework the tools are based on? So I'm not really convinced by that line of reasoning.

Bayesian methods don't perform so much better in the situation you just named. They're also more expensive.

The really shine in that they provide a really uniform vocabulary of producing new, more sophisticated models while "frequentist" methods usually rely on ingenuity to get to better models. So if you're actively exploring a model space and want to attach a bunch of assumptions and degrees-of-freedom to correspond with a theory you're testing... then Bayesianism is the way to go.

Theoretically, marketers are doing that exact process. In practice, they don't see that is a statistical process, though. Maybe someday a tool will bridge that gap successfully... but again, you're unlikely to get a huge advantage with Bayesian methods without that increased work investment.

I think is more because who is running A/B testing are not knowledgeable in stats, there are many other pitfalls that people fall into (in my personable experience) much worst than not using Bayesian rule, like sampling

Yea, I really agree with that statement. There seems to be much bigger problems that most people (starting out or moderately advanced) have with A/B testing. I hate when I see articles that talk about getting amazing results in "just 2 days."

I'd argue that Bayesian probability is more intuitive to the non-statistically trained. Once people know frequentist statistics, it's more difficult to talk to them about Bayesian results. I think you're right that the future could be more Bayesian if tomorrow's statistical wizards weren't inculcated into a frequentist mindset.