Isn't at least part of the problem with replication that journals are businesses. They're selling in part based on limited human focus, and on desire to see something novel, to see progress in one's chosen field. Replications don't fit a commercial publications goals.
Institutions could do something, surely. Require one-in-n papers be a replication. Only give prizes to replicated studies. Award prize monies split between the first two or three independent groups demonstrating a result.
The 6k citations though ... I suspect most of those instances would just assert the result if a citation wasn't available.
Journals aren't really businesses in the conventional sense. They're extensions of the universities: their primary customers and often only customers are university libraries, their primary service is creating a reputation economy for academics to decide promotions.
If the flow of tax, student debt and philanthropic money were cut off, the journals would all be wiped out because there's no organic demand for what they're doing.
Not in academia myself, but I suspect the basic issue is simply that academics are judged by the number of papers they publish.
They are pushed to publish a lot, which means journals have to review a lot of stuff (and they cannot replicate findings on their own). Once a paper is published on a decent journal, other researchers may not "waste time" replicating all findings, because they also want to publish a lot. The result is papers getting popular even if no one has actually bothered to replicate the results, especially if those papers are quoted by a lot of people and/or are written by otherwise reputable people or universities.