I dunno. Offhand, I guess whoever is citing the work would need to replicate it, but only if it's cited sufficiently (overall number of citations, considered foundational, etc...)
This could help your career by increasing the probability that the work you're citing is more likely accurate, and as a result, your work is also likely more accurate.
A typical paper may cite dozens or hundreds of other papers. This does not sound feasible. It honestly seems like it would worsen the existing problem and force scientists to focus even more on their own original research in isolation from others, to avoid the expense of running myriad replication experiments that they likely don't have the funding and personnel to do.
This could help your career by increasing the probability that the work you're citing is more likely accurate, and as a result, your work is also likely more accurate.