If you assume that 100% of the aether used to summon a primal goes immediately back into the land and it dies exactly here it was summoned, I doubt the Burn could come about...but do you assume that's true? What about all the aether that changes form and is expelled via magicks? And if primals are often summoned to be sent off to war against one another, they likely don't always die where they were summoned in the first place. The Warrior of Light rapidly hunting down and slaying primals in their home within a few days of them coming into existence is most irregular.
[tl;dr] Killing the Warring Triad a few moons back didn't suddenly make Meracydia nice again
As for "Why hate this?", there's always the side effect of aetherial imbalance, disruption of the natural order, and a whole bunch of general chaos, war, and death that primals tend to bring with them, especially since most of them temper actively, and most of the rest temper incidentally by virtue of their corrupting aura. It's a cycle of misery even if it doesn't go on long or harshly enough to turn your home into the Burn.
An old post by Koji Fox acting as the Metatron of Banri Oda leads me to believe that the "Essence" of most, if not all primals comes about like so:
[1] Living aether coalesces into a mortal soul and is born into the world from the sea. It gains an identity, lives, and dies as an individual.
[2] When such a being, its body slowly decomposes back into the corporeal aether and organic compounds that nourish the land. The living aether of the soul (USUALLY) is unable to resist the siren call of the Lifestream and rides the aetherial rivers back to the sea (allegedly through Mor Dhona). The rivers and the sea are extremely turbulent - a massive blender. It rends this frail coalescence apart, shears it into uncountable pieces, and those pieces find their way into new mortal souls again someday. (The Echo can potentially give souls such strength that they can maintain coalescence post-death, resist the call of the Lifestream, and even take over other bodies.)
[3] Every living thing leaves behind a story. Many are forgotten, but some are remembered. These memories are typically flawed, as all memories are. Mistbeard isn't even dead and the legends of his feats are of questionable veracity. (Ahem... The Sultana's Lap). Hell, some believe that even the faith of the Twelve originated or was heavily augmented by mis-remembered Warriors of Light. Sometimes, a story transcends the ages and grows more and more impressive - it becomes venerated ... worshipped. For example, the Allagan general that once commanded the Iksalion bioweapon legions becomes remembered as the Empress of Birds, eventually becoming the faith of Garuda, primordial force of the wind, Lady of the Vortex, goddess of the Ixal.
[4] During a summoning ritual, powerful faith or desire becomes a beacon for all the broken LEGOs of living aether that were once part of the thing that inspired the story that led to the faith. The Ixal call out, and all the broken pieces of the Allagan general are drawn to it. These LEGOs are then reconstructed into something new - you can smash a LEGO spaceship and make a LEGO submarine, but that doesn't mean the submarine is still the spaceship, or the spaceship reincarnate, or even that the submarine remembers being the spaceship. This living aether re-gathered is re-materialized into something new - the object of the faith - a shade of that being - an icon.
This is why Bahamut isn't Bahamut but looks more or less like him (ish...I know, the Celestial Dragon art piece, but grade on the Tiamat curve). He was brought back relatively quickly by his own kin. Shiva was a shade of a dead Elezen woman that Ysayle thought of as a saint and conflated with a mental image of Halone. Garuda wasn't even close. The accuracy of the facsimile is all over the place.
Ramuh should prove to be very interesting when we learn more about him. He seems to be part Rhalgr, part a mis-remembered bearer of Light, part the wise Old Man of the Wood; he seems to know things he shouldn't, or is that only because the Sylphs believe he does?
Pheonix and Shinryu are unique in this, as they seem to be Louisoix (who everyone was praying for to save them) and Ilberd (who everyone followed out of a desire to see the Empire suffer) seemed to become the core essences of their own primals. That Louisoix was still living at the time and died in the process leads to himself to refer to him as "no true primal" or in other languages "a quasi-primal", and this is partly why the twins fear his resummoning so much. The broken pieces of Louisoix will re-manifest as someone else's understanding of the Phoenix - a primal forsooth.
[5] During the summoning the essence re-materializes as that thing, and corporeal aether (crystals, environmental aether, the land's aether, etc.) are sucked dry to manifest the corporeal form the essence "ought" to have. That corporeal aether becomes the catalyst that keeps the essence together and in our world, and the cost of something that ought not exist existing is staggering. Even Omega can barely pay that price and chooses to run tests in its own pocket dimension until deciding for sure what it wants to make.
[6] Eventually, that primal is killed, separating the corporeal and spiritual aether. The spiritual aether goes back into the blender, the corporeal aether goes back into the land. The story remains. The story grows and changes. The story lives on.
[7] Repeat. Repeat. Repeat.