I think NHST is kind of overstated as a cause of the replication crisis.
People do routinely misuse and misinterpret p-values — the worst of it I've seen is actually in the biomedical and biological sciences, but I'm not sure that matters. Attending to the appropriate use of them, as well as alternatives, is warranted.
However, even if everyone started focusing on, say, Bayesian credibility intervals I don't think it would change much. There would still be some criterion people would adopt in terms of what decision threshold to use about how to interpret a result, and it would end up looking like p-values. People would abuse that in the same ways.
Although this paper is well-intended and goes into actionable reasonable advice, it suffers some of the same problems I think is typical of this area. It tends to assume your data is fixed, and the question is how to interpret your modeling and results. But in the broader scientific context, that data isn't a fixed quantity ideally: it's collected by someone, and there's a broader question of "why this N, why this design", and so forth. So yes, ps are arbitrary, but they're not necessarily arbitrary relative to your study design, in the sense that if p < 0.05 is the standard the field has adopted, and you have a p = 0.053, the onus is on you to increase your N or choose a more powerful or more convincing design to demonstrate something at whatever threshold the field has settled on.
I'm not trying to argue for p-values per se necessarily, science is much more than p-values or even statistics, and think the broader problem lies with vocational incentives and things like that. But I do think at some level people will often, if not usually, want some categorical decision criterion to decide "this is a real effect not equal to null" and that decision criterion will always produce questionable behavior around it.
It's uncommon in science in general to be in a situation where the question of interest is to genuinely want to estimate a parameter with precision per se. There are cases of this, like in physics for example, but I think usually in other fields that's not the case. Many (most?) fields just don't have the precision of prediction of the physical sciences, to the point where differences of a parameter value from some nonzero theoretical one make a difference. Usually the hypothesis of a nonzero effect, or of some difference from an alternative; moreover, even when there is some interest in estimating a parameter value, there's often (like in physics) some implicit desire to test whether or not the value deviates significantly from a theoretical one, so you're back to a categorical decision threshold.