I certainly haven't thought this through, but maybe this would make science more modular: combine the updates from M studies and calculate the new, combined update. Statisticians, does this work?
Typically, if you are practitioner in the field, it is not too difficult to identify instances where the result is highly dependent on the choice of prior.
The problem is, having tried it, this is much more difficult to do in practice.
On the first point this is equivalent to contracting a builder to build a house in any style.
Choosing a prior isn't always just about picking a wide band around 3 or a narrow band around 2. This is like the builder offering a choice of curtain colours from a swatch.
Making a commitment to implement any prior could be totally. Like the overcommitted builder being asked to reconstruct R'lyeh.