The Variability Chart platform is the only one that provides the option to get Bayesian variance components. It feels misaligned to not have the Bayesian option available in Fit Model as well. I do get questions from users at my company around getting different output for the same analysis, but using a different platform because any negative variance component may switch from REML to Bayesian without them realizing it when using the Variability Chart platform (even though there is some text with an explanation, they don't know what it means and/or don't pay attention). My default is to use the Fit Model platform with bounded variance components for random effects models (there is a 'soft' recommendation from JMP to do this on the last section of this page -- https://www.jmp.com/support/help/14/mixed-models-and-random-effect-models.shtml).
If the Bayesian option is available in Variability Chart, I'd like the flexibility to leverage it with a more flexible model structure in Fit Model as well.
There has been some good work done by the JMP folks to investigate the utility of the Bayesian option (mostly because negative variance components are really confusing to, well, everyone). Here is one link, which looks at a Measurement Systems Analysis application. My assumption is that these principles can apply to all random effects models in general.