Earlier quoted context omitted.
Replication is over-emphasised. Attempts to organise mass replications have struggled with basic problems like papers making numerous claims (which one do you replicate?), the question of whether you try to replicate the original methodology exactly or whether you try to answer the same question as the original paper (matters in cases where the methodology was bad), many papers making obvious low value findings (e.g.…
So then, how on earth does this stuff even get published? What exactly is it that we're all doing here? If a finding either cannot be communicated enough for someone else to replicate it, or cannot be replicated because the method is shoddy, can we even call that science? At some level I know that what I'm proposing isn't realistic because the majority of science is sloppy. P-hacking, lack of detail, bad writing, bad…
The amazing thing is that it all works out in the end and science is still making (quite a lot of) progress.
That's also the reason why we shouldn't spend all of our time and money checking and replicating things just to make sure noone publishes fraudulent/shoddy results. (We should probably spend a little more time and money on that, but not as much more as some people here seem to suggest).
Most research is in retrospect useless nonsense. It's just impossible to tell in advance. There is no point in checking and replicating all of it. Results that are useful or important will be checked and replicated eventually. If they turn out to be wrong (which is still quite rare), a lot of effort is wasted. However, again, that's rare.
If the fraud/quality issues get worse (different from "featuring more frequently and prominently in the news"), eventually additional checks start to make sense and be worth it overall. I think quite a lot of progress is happening here already, with open data, code, pre-registration of studies, better statistical methods, etc, becoming more common.
I think a major issue is the idea that "papers are the incontestable scientific truth". Some people seem to think that's the goal, or that it used to be the case and fraud is changing that now, however, this was never the case and it's not at all the point of publishing research. I think a major gain would be to separate in the public perception the concepts, understanding and reputations of science vs. scientific publishing.