Great Post. I am thinking that science is like a bilevel process with experiments performed using frequentist methods but the scientific consensus emerging Bayesianly.

Frequentism is really only appropriate for formal experiments where you decide beforehand what you are going to do (with randomisation, controls etc) then do it and get the results. This formalism (should) have the effect of getting people to do their experiments properly!

The scientific consensus emerges from scientists reading papers and updating their internal models of how things work. A scientist may weight a paper according to how likely they think the results are and how well the study is done.

Overall, this bilevel process works well.