It is one of the boxes that a job needs to tick. Not all boxes need to be ticked, but at least some do.
This 'Modern Assassin' job also uses weapons that other jobs already use.
People like to say "but we already have multiple sword jobs" but the fact is each job uses a completely different type of bladed weapon that we like to call 'swords'. In truth, a Katana is not a sword, it is a Katana. And that's the thing, this 'Modern Assassin' doesn't just have a 'sword' or a bladed weapon, it has a goddamn Katana! The exact same type of 'sword' as Samurai, so you can't even make the 'other jobs have swords' argument. This would be like making another job that uses a Astrolabe or another job that uses a Gunblade.
So that's one box that 'Modern Assassin' fails on.
Next is a unique job identity. From what I can tell, 'Modern Assassin' steps on the toes of Samurai, Ninja and Machinist all at once. It doesn't really bring anything new to the table, rather it combines three different jobs into one. What is the lore? What makes it worth combining these three jobs together exactly?
While this one is a bit more 'personal opinion', I really can't see it ticking this box either. Frankly, it strikes me as something that should be in a Persona game, not a Final Fantasy with a high fantasy setting like XIV.
Finally, unique job mechanics. What would make this job, and specifically a job that uses a gun and a sword, play in such a different and unique way that another concept with different, more fitting lore, and weapons that aren't already taken, couldn't do just as well?
'Modern Assassin' doesn't measure up to any of the metrics that they use for choosing new jobs. If i felt it did meet the requirements of even just one, I'd let it go by without a comment.
As for Spellsword and Gunner, these are also already taken.
Red Mage has cannibalised the 'Spellsword/Rune Fencer' concept by way of having multiple skills taken from the XI Rune Fencer job, and an enchanted melee combo.
That's not to say other parts of the 'Spellsword' concept couldn't find a home in a new job, perhaps something like a 'Mystic Knight' from Thavnair that uses Maces instead of swords. But it wouldn't be a Rapier wielding, blade enchanter.
Likewise Machinist covers Gunner in every conceivable way. If there's another unique mechanic you can think of for 'Gunner' then it can likely be used for any other ranged weapon just as easily, like a Crossbow, which would make it more unique than an alternate version of Machinist. Which by the way, isn't new to XIV as you say, Machinist has been a job in the Ivalice games since they started, predominantly as the one and only gun job, and it didn't even have other machines then, they came from VI's Edgar. So 'Machinist' is literally FF's answer to 'Gunner' in every way.
You say the game is missing these 'basic jobs', but they are missing specifically because they are too basic. It's the same reason we don't have Thief or Archer as 'jobs'. Thief doesn't have enough unique identity to make it a full job in FFXIV. It worked in past games because all jobs needed in those games was one unique skill. That's why it was amalgamated into Ninja.
Same with Archer, shooting arrows isn't enough on its own, so it was bundled in with Bard, because both their weapons use 'strings' with a similar aesthetic.
Astrologian too, combines Astrologer, Gambler and Time Mage. Although I'm sure they could have come up with a full job concept for Time Mage as a DPS, Astro as a healer probably needed more going for it so they took parts from Time Mage, and after all, Orran's Astrologer was basically a special Time Mage, like how 'Magus' is typically a special Black Mage.
Going a bit less obvious now, we have Warrior, who combines classic Warrior with Berserker and Viking.
Plus Scholar, which uses the namesake of a job from FFIII, but is essentially an Orator with a fairy as a pet.
All of the concepts that went into these jobs, were not enough to stand on their own, so they found homes in job combinations.