There is also unavoidable subjectivity in making the choice of model, data, etc.

Yes. You've hit the essence of the problem - the choice of a prior. The scientific method gives us a way to choose a prior that fits reality. You are claiming something different, that our prior is based on subjective choices. Yep, those are both ways to choose a prior. But only one is guaranteed to be valid. Do I even need to mention the appalling history of base rate neglect in medical research? Neglecting priors leads to bad decisions.