Poll: Which of these FF jobs would you like to see added to XIV next? (Post ShB)

[MirronTulaxia]

Warrior has axes and hammers (the Tomra axe is a hammer) = Viking

So, as a starting point, every single one of these jobs could be a different role from the ones listed. Which is a huge blow to "these jobs are in the game". Outside of that...

Viking has elemental effects they could add (FFTA2) which Warrior doesn't touch.
Summoner is effectively the same thing as Necromancer (so much so that they could pretty easily just turn it into Necromancer and make a proper Summoner), but there are other ways they can do Necromancer that aren't the same as a DoT focus.
Time Mage has a lot of dimensional magic that Astro doesn't touch. Astro is more stars and fate while Time is... well, Time and Space. The only major overlap is Gravity, which is easy enough to handle.
Elementalist is more broadly just an elemental spirit user. There isn't any reason they couldn't make that work differently from Black/Red.
Cannoneer/Flintlock use heavy artillery, which isn't how Machinist works.
Corsair has a luck effect that Machinist doesn't use.
Dragonkin is more about being a Dragon, while Dragoon doesn't do much in that area. It's closer to being a specific Morpher variant.
Broadly "guy with a bow" can be used in different ways than "DoT Summoner" and... I'm presuming Bard? Bard is the closest of the two, but Summoner? Makes no sense.
Magic sword guy is pretty different from Squall the job. As an obvious point one of them... uses magic. Dark Knight/Paladin are closer, and those aren't really magic knights so much as knights who use a tiny bit of magic.
Sage is "master of magic". You could build this any number of ways. None of them are specifically Conjurer.
Storyteller doesn't use books specifically, they use all weapons equally well. And if we wanted them to use books specifically again that really doesn't matter, there are plenty of ways to build someone that aren't specifically DoT's or Shield Fairy.
Animist/Morpher, even presuming you specifically added Beastmaster, don't have to work like Beastmaster. Especially as it's likely to be a Limited Job. There is a big difference between using monsters and turning into one. But as Beastmaster isn't even in the game you're jumping the gun.
Arithmetic/Mascot/Psychic/Storyteller have plenty of ways to be built. Arithmetic can do math themed attacks, Mascot can do cute mascot attacks, Psychic has the entirety of psychic things to work around, and Storyteller could work with lore and stories as a theme.

In comparison? Puppetmaster/Beastmaster would just be Summoner by the standards you're using, and Chemist would just be Astrologian or Machinist. Note that I don't agree with those, but there isn't any reasonable way to say all of those are the same but those three somehow aren't.

Really it just seems like you are saying using the same weapon means they're the same job, which is absurd.

[Seraphor]

Viking has elemental effects they could add (FFTA2) which Warrior doesn't touch.

Warrior actually uses a lot of nordic names and it has similar elemental animation effects, lightning and fire mainly. It seems quite obvious to me that Warrior in FFXIV is a mash up of Viking and Berserker, which writes off both of those being their own job.

Time Mage has a lot of dimensional magic that Astro doesn't touch. Astro is more stars and fate while Time is... well, Time and Space. The only major overlap is Gravity, which is easy enough to handle.

Astrologian is another mash up, Astrologer and Time Mage. You've mentioned Gravity, but then you also have to consider that reading fate, predicting and changing the future is an avenue of time manipulation. I don't know how you can argue that reading the stars and changing fate aren't basically Time and Space magic.
Once again, they put these two roles together because they didn't feel they were enough on their own to warrant a full job in FFXIV given the different format to other games job systems.

Cannoneer/Flintlock use heavy artillery, which isn't how Machinist works.
Corsair has a luck effect that Machinist doesn't use.

Machinist does use heavy machinery, and a 'luck effect' isn't enough to build a job around, especially when it shares a weapon with an existing job.

It seems you've misunderstood the job philosophy in this game. Jobs have to be well-rounded to a certain degree, and not one-dimensional, plus need to have their own unique identity and ideally a unique weapon. This makes a lot of classic jobs unsuitable on their own, which is why we have job mash ups in FFXIV, like Ranger/Bard.

Puppetteer/beastmaster probably would just be Summoner if it were a normal job, which is why the Limited Job system creates an avenue for Beastmaster to have a unique identity.
Chemist wouldn't be anything like Astrologian because it's an entirely different job aesthetic and lore, and it can get away from Machinist by being an entirely different role.
These are the things you need to consider, these are the things SE consider when coming up with new jobs.

And yes, weapon is a big part of the job system, given that you change jobs by changing weapon.
The only jobs that have similar weapons are: SCH and SMN, different roles, and WHM and BLM, again different roles. Hence why Chemist, as a healer that uses some sort of firearm, could work, while Corsair, a ranged DPS that is basically a Machinist without machines, wouldn't.