On the other hand, this seems like a super interesting path for an (unglamorous) PhD -- replicate the N most important findings in a field, subject to some restrictions (maybe focus on the ones that are "easy", or haven't been replicated yet, or the ones that could be patched together to make an acceptable PhD thesis). This sort of stuff really appeals to me, I think I might end up doing something like that in 5-10 years.
I share your enthusiasm for this. Creating a map of the most influential research across all the fields to identify the highest priority work, any work replicating that work or validating that work by building from it would be a good start. Ideally funded by governments, but institutions, companies, and individuals could put up bounties for replicating particular research.
I think you're right that this will be the most common objection, but wrong that it will be exceedingly difficult to find an advisor that would support this. I assume that if you _can_ overturn some foundational result, you won't face criticism over novelty (potentially you can argue that overturning important accepted results is inherently novel). Then the rest is just math:
Assume that n% of foundational studies are demonstrably incorrect if replication were attempted. Then if you replicate X foundational studies, there's a 1 - (1-n/100)^X chance that you'll show one foundational study to be incorrect. Then I think you just need to find an advisor who believes the incorrectness rate n, and the replication attempts X is high enough for you to revert a foundational study over the course of your PhD.
