Right. White Magic is a seperate school of magic that piggybacks on Conjury by virtue of the ones who were entrusted with that knowledge already being CNJs themselves (ala the padjal, who were made custodians of Amdaporian white magic knowledge by the elementals as a safe guard against those trying to seek it out without permission).
Edda was not using White Magic in Tam Tara HM, she was using necromancy (which is actually void magic) to summon voidsent (in the mistaken belief it's reviving the dead) - presumedly given to her by whatever it was that pushed her towards the darkness (most likely an Ascian). It just shows how taboo the subject of necromancy in Eorzea really is (and why a Necromancer class will never be playable). But anyway...
It wasn't just the 4th Calamity technology and science were destroyed, the aftermath of the 6th Calamity after the floodwaters abated any kind of knowledge or technical idea, whether magical or technological, was purged as a backlash against the cause of the Flood (the War of the Magi), to the point even those who just happened to be literate were lynched, because the layman could not tell the difference between a mage or a scientist. Not surprisingly, it caused Eorzean civilization to collapse into total barbarism that took millenia for the realm to actively recover (and it still has not fully reached the same level of progress that existed in the 5th Astral Era, let alone the 4th with the Allag and their cyberpunk levels of tech, not helped by the 7th Calamity pushing things back even further).
This is why Sharalyan is so elitist and zealous towards guarding their knowledge stores, they don't want a repeat of the 6th Calamity to happen again (unfortunately that just made them look arrogant towards other nations), Louisoux and the Circle of Knowing becoming condemned by the Sharalyan elite as total pariahs for advocating a more open policy towards dealing with the Eorzean citystates, and especially, the dissemnation of ancient knowledge and wisdom to Eorzea's nations.
Sorry to jump back to this but it is correct that most disease seems to be usually taken care of by magic or herbal/alchemical medicines - an example is the so-called 'wasting sickness', a potentially fatal disease that was at one time at epidemic levels among the hyuran population of Gridania, although it's stated that conjury spells exist now to cure the affliction (Esuna?), herbal treatments are still produced and stockpiled for hamlets in outlying areas as they are considered valuable in case a CNJ with the right skills is not available to treat the patient (this was mentioned in a very early sidequest in Hyrstmill).
However, having said that at the first Fanfest Ferne himself mentioned about an ultimately abandoned plotline for 1.0 that dealt with a disease called 'the green death' that was spreading like wildfire through La Noscea and Limsa, and that there was no effective treatment available, with quacks and snake-oil salesmen touting all sorts of remedies for it to the desperate that did not actually work, but it was never actually added to the game. It's possible this served ultimately as the basis for the tonberry plague in ARR which also was untreatable (although that was called 'the sickness from the sea' and which had a magical, voidsent cause).
True, but in that specific reference to humorism the game itself even states that in universe it's possibly load of bunk with the description for the chigoe larva minion (which also revealed what a chirgueon actually is - it's not a fantasy name for a surgeon, but a quack doctor that uses a blood-sucking parasite to drain small amounts of blood from the patient to supposedly drain 'dark humors', in this case, a chigoe); that far from helping the patient it was discovered that the patients were contracting additional diseases and problems as a result!
The word' 'leech' also seems to be used in a similar manner - a 1.0 main story quest used that term to refer to a doctor when seeking medical treatment, and there is of course the SCH spell 'Leeches'. So yeah, the game kinda zigzags whether humorism really does work or if it's just a convinent way of explaining something coincidental in medical terms that has a more mundane, scientific explanation.