Primals Unquestionably Bad

[Enkidoh]

A few things to clarify here:

7. garuda's summoning of ifrit and titan (interestingly, no crystals were used, instead it required multiple sacrifices of kobolds and amalja, nor was the summoning done by the beast tribes, it was a primal summoning two others)

Watching the scene in question and looking at screenshots, it's apparent that Garuda herself wasn't the one who summoned Ifrit and Titan in that scene - she merely tortured the amalj'aa and kobold prisoners to the point they pleaded to their respective primals to save them.

From what I could gather, this was only possible because the Howling Eye was practically saturated in aether - it was an aetheric cyclone in a sense (I mean, unlike the other Primals, Garuda herself still continuously remained corporeal even after being defeated by the player and having her crystal forcibly torn out of her by the player's Echo) so thus all that aether could make it very easy for any Primal to appear in the right circumstances, which Garuda seized on by pushing the Ixal's beastmen prisoners over the edge - it was only when Gaius showed up, shot dead all her Ixal followers and Ultima Weapon absorbed her and the other two Primals did she disappear. So yeah, this was not a special way of summoning - merely the 'normal' way of summoning a Primal done out of desperation.

CNJ and WHM are the big exceptions, the whole point of the CNJ questline is to cement the fact that they use their own aether like THMs, but rather than regaining aether through meditation, nature gives them their aether back, if a CNJ uses too much aether without accepting more from nature, they overexert themselves and die, however, the amount of aether that they are allowed is purely at the discretion of the elementals, if you are using too much aether, they'll probably just refuse to give you any more until you stop being so wasteful (amusingly, that's probably put sylphie in the elementals good books, considering that she tried to stop using magic at all fearing that she's hurting the elementals by using ANY magic).

in the past, when there was no regulation for WHMs, EVERYONE was using full on white magic with no regard for what would happen, both WHMs and BLMs were taking aether directly from the lifestream and the sheer amount of magic used in the war of the magi brought about an umbral era. now, BLMs all use the THM's methods of restoring aether, whilst lorewise, WHMs are strictly regulated (canonically, you are the only non-padjal WHM, and you are one of the few remaining BLMs), CNJ are WHMs regulated by the elementals, rather than just ripping magic from the lifestream, whilst WHMs are free of such restrictions on the use of their magic, hence only the padjal, the ones that the elementals specifically choose, are allowed to become WHMs (and yourself, by virtue of being A-Towa's heir, and even then, one of the two padjal was fairly worried about the prospect)

Actually, that's not entirely correct - you've clearly mistaken Sylphie's unique healing ability with Conjury as a whole in the CNJ quest line. Conjury has been constantly mentioned both in 1.0 and ARR, and out of universe (in other words, on the FFXIV website), as borrowing the aether from the environment in order to then weave it into spells. To do so a CNJ has to open their minds to the elementals in nature - someone who is closed minded however cannot conjure - this was actually Slyphie's dilemma at first - she refused to open her mind to nature and instead preferred to go around healing people using what could be best described as the traditional White Magic ability 'Sacrifice', like her mother before her. E-Sumi-Yan actually mentions early on how useless at actual conjury she really is - that she cannot conjure so much as "a single whiff of air or pebble."

Eventually though, through the player's influence she realizes the power of nature and is revealed to have a particular talent for hearing the elementals with particular clarity, a 'hearer' as they're called. Hence she eventually lets go of this stubbornness, focuses on nature around her and finally can conjure effectively. White Magic is technically therefore a separate school of magic whose inner workings are not elaborated on,although it does seem to go hand in hand with Conjury, given the padjal are the only ones who remain with the knowledge to use White Magic (they use it in specific rites as hearers).