Class => Job => ???

[dinnertime]

Conjurer and Thaumaturge

Conjurer had Protect, Shell and healing spells in 1.0 so it fits for them to evolve into White Mage, and in most cases WHM can use some element-aspected spells. Not sure if they were referred to as healers in the 1.0 lore though.
But yeah, how Thaumaturge becomes Black Mage is a bit of a stretch when Conjurer had all the element-aspected spells at 1.0 launch but it's a thing of the past now. It's just aesthetic though.

Summoner and Scholar

For Summoner...yeah I feel like they should rewrite the lore to unrestrict the variety for summoning, but before that they have to give the job at least Leviathan, Ramuh and Shiva summons.

And yeah, Scholar is more of a war tactician and medic actually than a literal bookworm. It makes it interesting in my opinion.

Thancred still calls himself a Bard

I think he's referring to him being just a bard and not Bard as a job.

I can't say anything about Arcanist or Machinist though since their lore didn't interest me that much to remember, but I should read on the lore of every job to refresh my memory.