So because I'm bored, I'm gonna break down most of the jobs I've seen so far in this thread:

Onion Knight....I could honestly see this as a Limited Job designed around a "make your own job" theme that could be an interesting PvP thing.

Mime, when you think about it as a baseline concept, is just Blue Mage without anything that makes Blue Mage fun and/or interesting. If you do not find Blue Mage fun and/or interesting, also yes.

Berserker we already have. It's called Warrior.

Necromancer, in terms of game lore, is oddly just a Black Mage on steroids. While it's possible to have something like a Necromancer in FFXIV, it likely wouldn't look like what we would consider to fit a western description of one, spawning something like ghosts or spirits out of the nether rather than corpses out of the ground due to both censorship concerns and the aforementioned game lore. It might even be renamed to something like Reaper or Druid--I mean seriously, have you seen the stuff RL druids did in the past? Holy crap.

Arithmetician we sorta have in the form of Scholar and the base class Arcanist to a degree. Unfortunately, devs learned the hard way during ARR via the original Lustrate ability that anything percentage-based is actually quite terrible to implement, being incredible at the start and then staggeringly subpar as gear levels go up.

Viking, surprisingly enough, can still be implemented. In addition to Viking being a bit like Warrior, it also came with some Rogue-like abilities along with Tsunami and an assortment of Thunder spells. If Viking were to instead focus more toward the magical aspect rather than being the usual brute with spells like how Dark Knight is now, then it could definitely happen in the game.

Chemist may not be released as the salve-maker throwing vials at people's faces, but it'll happen. As long as people won't shut up about it, Chemist will happen via some sort of variant (hopefully as something like Cannoneer from FFTA2).

Plumber....maybe the reconstruction of Ishgard will finally bring in some much-needed toilets. Maybe it'll involve educating the nobles not to try and flush their lowborn.

Time Mage is a curious possibility now that Astrologian has been stripped of most of its time-based abilities. It also wouldn't be the first Square-Enix game to have both Time Mage and Astrologian in the same game.

Geomancer, Beastmaster and Puppetmaster I think could happen, but not like anything we've seen before out of those jobs. They would also join the ranks of Blue Mage and Eureka among the list of reasons why diehard FFXI fans need to stop suggesting things for this game because for the love of the Twelve, this is not Vana'diel and please stop ruining this game because IT'S NOT YOUR PRECIOUS CHILDHOOD GAME DEREN--er, whoops....