It's possible that occasionally, we'll waste our time looking for explanations of things that really are coincidences. But since this will be rare, it's worth looking for explanations anyway.
There seems to be a contradiction in terms in my approach: how could I conceive of gratuitous coincidences that are outside of the causal network necessary for life to emerge and at the same time expect they are not entirely independent from necessary coincidences ?
Both necessary and superfluous coincidences could be manifestations of "structural coherence" and correlate to the degree of "order" or "complexity" of the universe. I'm unsure about my choice of words (knowing that there are precise ways to measure those), but maybe what I'm trying to grasp at is that emergence of observers is a hard problem, as shown by the very small margins the fundamental constants need to sit within for this to happen. Our existence isn't attributable directly to the singular values they take, but to the expressivity they allow, carbon chemistry being an example of that.
Maybe the laws of physics and fundamental constants operate like a sophisticated construction system. Like Lego, they offer increased degrees of freedom and expressive potential, but this very complexity comes with the cost of enabling marginally legal or "quasi-valid" configurations. A high level of compositionality inherently generates possibilities beyond strict necessity—introducing both meaningful structures and potential anomalies.
We could almost put this to test by measuring how easy it is to find non-sensical quasi-equations in the laws of physics, comparing our set of fundamental constant values with randomly generated ones. I guess distinguishing false coincidences and false gratuity would constitute the wall preventing us from doing so.