How exactly do Calamities and Rejoinings relate to each other?

[Rocl]

If the Ascians consider it a Calamity, it's probably enough. They have canonized the Seventh Umbral Era and its preceding Calamity as a victory and an Ardor, so it seems have been a Rejoining, yes. Elidibus muses if Minfilia surviving the Ardor was by Hydaelyn's direct intervention as early as 2.1--we can safely assume he's referring to the most recent Calamity before anything else here. (And in the very next quest Elidibus mentions "they survived the Seventh Ardor;" so yeah, that Calamity, no matter how wimpy or mitigated, Rejoined a Shard.)

The Floods seem to be bad because when a Shard experiences a Flood, it can no longer be Rejoined. This leaves a lot of questions, like, "how many Shards is enough to revive Zodiark?" because the answer can't be "All of them" if one is permanently incapable of being Rejoined.

Void of its aether, the Thirteenth could no longer be rejoined with Hydaleyn, ultimately losing its value to the Ascians.

Now that my cursory research is done, let's try to put this more succinctly:
A Void of any flavour is bad. The shattering of reality and expulsion of Zodiark carved up the Aetherial Sea into 14 pools. To undo this, the pools, and all of their aether, must be added back to the Source. A void is devoid of aether, so it's worthless. How a Flood of Darkness and a Flood of Light differ in their creation of a void seems ultimately meaningless, because there's no aether left. Whether Rejoining a Flooded Shard with the Source would screw it up... probably? But it's just not worth doing--there's no benefit for the Ascians to do this.

The Seventh Umbral Calamity signaled a Rejoining. No matter how localized it was due to Louisoix's intervention (and let's not forget it did disrupt the Source's aether enough to render linkpearl communication useless for a few days, iirc) it still ultimately resulted in a Shard's aether being folded back into the Source. Both our allies and enemies agree on this matter--the Ascians refer to seven Ardors even when we're not around, and the Encyclopedia Eorzea refers to the Scions and Students both having come to the same conclusion. Each Calamity ushers in a sort of Dark Age, and we're left with few records of what happened earlier. While the Seventh Umbral Era was short, and it was localized, it's important to note we don't know how ANY Calamity affected the rest of the Hydaelyn... outside of, like, the Fourth Umbral? Everything pre-Allag is pretty much unknown, we have legends and lores about Calamities of Wind, Lightning and Fire and descriptions of such... but we know nothing of those Eras, their peoples, their stories. It's impossible for us to know how far-reaching those Calamities were. The Fourth Umbral might've had global implications simply because it ended the Allagan Empire which had conquered the Three Great Continents & Meracydia (and probably much more); we don't know how far the earthquakes actually went--the power vacuum alone would be destabilizing enough. The Fifth and Sixth are the same--we know the seas probably turned to ice in some places for the Fifth, and we know Eorzea was flooded in the Sixth but... those could still be localized events! Especially the Sixth Umbral Era.

I think it's telling that throughout our time in Othard, we very rarely, if ever, hear about any of the Calamities in their histories.