I think this is the proper way to think of it. You figure actual age of Hydaelyn is approximately 12,000 years and there's only been 7 Calamities, that's pretty close to 1800 years per Calamity on average. However, we know the age of Allag was only approximately 5000 years ago so that means the first 3 Calamities took over 2000 years each (though I guess I wonder if we should include the failed Rejoining of the 13th, which would put it back closer to 1800 years per Calamity.) There's evidence that they've gotten better at causing Rejoinings, but not by much.
We also know a few more things that make the situation unique:
1) by mitigating the damage of the 7th Umbral Era, the world appears ready again already for another Rejoining
B) in the past [1 year/100 years] over half the Convocation has been killed: Nabriales, Igeyorhm, Lahabrea, Emet-Selch more or less by us (Lahabrea is debatable but considering someone important considers it's our fault....); Loghrif and Mitron by our partial soul; and the 2 masks Gaius spurred by us defeating him—to Elidibus he can pin roughly 8 deaths on our/our soul's shoulders. There's also Emmeroloth gone [maybe?], so the number of Ascians, by the time of 5.3 is pitiable at best. The Convocation, already perpetually down a member, is missing nine of its number if you include the defector.
(I included Ardbert and Gaius' killcounts, because apparently we're also to blame for Lahabrea. Even without those 5, we're still winning the "most deadly to Ascians" award with 3 kills.)
5.3 MSQ
Now think about it, Elidibus has the world ready for a Rejoining. He's tried to tip the scales three times already and been beaten back—the Dragonsong War/Thordan; Ilberd/Shinryu; Zenos hijacking/Ghimlyt. He already broke out a "secret weapon" in Emet-Selch, which we know was the right call from the Exarch's future knowledge, and through it all we botch that up for him too. So his plans are in shambles AGAIN, and we kill the last Unsundered aside himself.
The world is ready for a rejoining, he wants to strike while the iron is hot. He's emotional and feeling cornered—impatience born of loneliness is definitely the right read here, I think. The comparison to Nidhogg is probably apt too, Nidhogg raged for a thousand years after the death of Ratatoskr; Lahabrea and Emet-Selch being the last Unsundered and killed within [1 year] has no doubt made Elidibus think he needs to deal with the problem of the Warrior of Light now. Who knows what else we could accomplish if he waits? If Elidibus retreated to the Rift and waited until the Warrior of Light died of old age... we'd be reincarnated somehow, and he'd have the problem of wrangling at least 6 new Ascians. Igeyorhm, Nabriales, Lahabrea, Emet-Selch and Gaius' two masks for sure—maybe Emmeroloth, Logrhif and Mitron too.
All the waiting while the Warrior of Light expires still necessitates he keep whatever aetherial balance is necessary for a Calamity in check for all that time, and also stymie our attempts at wiping out the remaining Ascians who we are probably going to be specifically targeting. So it's not like he could just pop off and take a nap... there would still be work to be done, or just write off this Calamity-ready World and keep a strict leash on all other Ascians.
Sure, a new Azem might not be as effective as our Warrior of Light, and he may be missing the Blessing, but we've learned if nothing else mankind is resilient in the face of seemingly insurmountable odds (after all, after succeeding in the Eighth Rejoining and the Warrior of Light dying, mankind STILL found a way to undo it—no doubt the ability to stop that from happening also informs his decision making regarding the Tower).
Even for someone billed as a master tactician, waiting only adds more variables and exponentially increases the amount of eventualities he'd have to plan for.
I admit, however, that I haven't reviewed the 5.3 cutscenes as diligently as some others so my analysis may be less than perfect. I've also walked away and come back to this post a few times, so I'm sorry to ramble!
In short: waiting out the Warrior of Light probably isn't the easiest solution. It might set the Rejoining back a couple decades... or nearly a millenium if the Land heals. Furthermore, mankind's most dangerous weapon to the Ascians; the knowledge of what they are and how to deal with them is definitely going to persist until the Eighth Calamity passes (unless he takes an active role in, like, sinking Sharlayan which puts him at risk).