I agree, and suspect many people (outside of the statisticians who have had the time and space to digest the philosophical underpinnings) who claim to love Bayesian methods do so because they have been told it's the right thing to love. There are a lot of hand-wavy explanations out there that tell you what each side believes, but I have yet to see something that truly ELI5s it.
Well, maybe I'm an exception since I am a statistician, but Bayesian techniques allow me to do things which are simply impossible with frequentist tools. To be fair, I use both approaches just about every day.
"I use both approaches just about every day" is the only sane answer here. Different tools for different jobs. What would think if you met carpenters who described themselves as "Hammerists" or "Sawsallitarians"?
Sure, but there's nothing which would prevent you from addressing that from a Bayesian perspective. In fact, Bayesian particle filtering techniques would probably be a great tool for "on-line" quality assurance.
I'd think they just made it clear how to choose one or the other based on whether I wanted something built and/or destroyed, as opposed to whether I just wanted it cut apart. ;)
