I mean, the issue with "well White Mages only use Light because of Shadowbringers stuff" is that we have Sin Eater Conjurers. They still use Earth and Wind. If Sin Eaters, beings purely of light aether just about, aren't turning their spells into Glare/Dia and instead get Sanctified Stone or the like then the obvious answer is that the White Mage is just changing to Light themed things.

And I'm not really sure where you're going with the names and such, just seems kind of odd. Anyways, Fire/Ice (Thunder is kind of weakly represented in Black Mage) are in Black Mage. Light is represented in White Mage. Thunder/Wind kind of get more of a role in Red Mage than other elements, but it's kind of a weak focus, maybe they'll add more to it. I doubt it but I feel it would kind of help it stand out elementally speaking as opposed to the more hodgepodge they currently have. The others are even more weakly represented at best, and I wouldn't call any of them "all elements", certainly not Summoner at least currently. Water/Earth could certainly see some focus if Geomancer becomes a thing, though I'll add to that this is looking at it purely in an offensive standpoint, as most of these elements are represented outside of damage dealing stuff, and Dark for Astro is... eh, kind of weak too.