Science is a lot like sausage processing. The end result may range from the quite passable to the quite good, but if you actually saw the raw materials and the process, you'd be more discriminant on what you put in your plate.
If I publish something claiming bacteria has a gene X that produces phenotype Y, then a subsequent study that transfers gene X into a different bacteria must also observe Y. Otherwise something is fishy, and often the second set of researchers will go back and reexamine the original result.
It's rare that work in science is directly, point for point replicated, it's unsexy, expensive work. The fact that the harder sciences have somewhat of a built in control mitigates but by no means eliminates the risk of bad science surviving.
I can't think of an analogous process in the softer sciences. Seeing if a phenomenon is replicated in a different context does not implicitly re-test the original work in the same way.
The problem with results like "ego depletion" is that their utility is fuzzy at best. With no clear application, we don't have a body of practical results using it.
There is no guarantee (and it often isn't the case) that the phenotype observed in the first organism is purely the result of gene X; its effects may be context-dependent.
To take this a little further, I think it's plausible that a soft scientific question differs from a hard one specifically in terms of how easy it is to separate the phenomenon in question from its context.
The reality is that the end results are usually terrible and a lot of science out there is straight up junk science designed to chase grants and to lean on journal biases to get published, especially in the social sciences. The problem is we don't really have a better alternative so working with a clock that's right twice a day is much better than having no clocks at all. We might have hit organizational limits on how well we can do science on this level. With funding comes politics, with journals comes bias, with publishing comes perverse incentives, challenging big egos is difficult, unknowns have to 'pay their dues', small universities and institutions don't have influence compared to their larger peers, the sometimes political tenure process, etc.
Hell, the article itself even calls out Carter's relatively young age or for not being tenured in an almost "Can we trust this young nobody," way.
That's normal science at work. Old sages are biased, like everybody else. Fortunately, they are mortal too [1], and science keeps moving forward 'one funeral at a time', as the saying goes.
The problem is with people who want to substitute faith in the Divine Providence of God, with faith in the (eventual) Unfailibility of Science. We are just a bunch of social primates, after all. We were never meant to peek into the Deep Mysteries of Existence, anyways... which does not mean we cannot use our relatively advanced intelects to figure out a bunch of clever and useful tricks.
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[1] Something that is nightmare fuel to me is that one day we are going to stumble upon some serious life extending technology, and then we will all end up under the thumb of a bunch of ancient, obstinated fools who cannot/won't accept the limits of their own leadership skills.