When it comes to balancing classes in a Trinity game, the hard math that comes from theorcrafting and practical application comes down to the right tool for the right job. The 'strongest' jobs aren't necessarily those with the most damage, but those who deal with the most mechanics / reduce the overall strength and difficulty of the encounter.
The reason that FF14 values damage so much is that the player's ability to influence the encounter is generally limited to some hard binaries, with DPS being the only scaling adjustment. ("Skip soar or disband"). The hard binaries are generally tank busters and healing requirements via the raid busters. The hard enrage, while adding a suitable layer of tension, also removes some ability to compensate. Being 'less efficient, more consistent' is generally the motto when it comes to encounter puzzles in other games, and really only applies in FF14 as gear scales the player up, allowing the 'less efficient' to clear the same hurdle.
"DPS is king" because it's the only real agency the player has in influencing the encounter.
So who gets the most DPS?
Generally speaking, it's usually those who bring the least supplemental tools.
One would expect this means Black Mage, Samurai, and Machinist.
As a secondary property, it's also those who have the most constraints. The Samurai must be in melee and must hit positionals to maximize damage. The Black mage must complete a cast in order to deal damage, but does so from any range. The Machinist has none of those constraints.
So your expectation is that these three jobs deal the most damage, but the order of their ranking should be Samurai >= Black Mage > Machinist. The thresh hold and difference between them is generally where the contest is, but the idea is that encounter design varies enough, and player capability matters enough, that the three can leap frog around these on-paper rankings.
Almost done.
But we also run into the problem where each of those jobs also have 2-3 other jobs who fall into the same category, who bring a variety of non-damage oriented tools along with varying effective raid damage increases.
So we have some things we have to consider.
1. The jobs who bring extras cannot deal equal or greater damage. That is immutable, or the jobs who bring nothing else are obsolete. "Extras" are non-damage oriented tools or capabilities.
2. There are four slots for them. At a bare minimum the value of a given role must at least be the equivalent of going from 105% stats to 104%.
3. A job's given strength should be assumed over a variety of encounters, not just ones tailored for it. A tailored encounter should be its chance to excel, not its chance to be passable.
With this in mind, lets start with 1.
The Samurai cannot be outclassed by Monk or Dragoon. The Ninja's supplemental tools have largely been removed, with Trick Attack mostly just being lip service. That said, compared to the other jobs, Ninjutsu affords it more robust capability from out of melee range, so in fights without 100% uptime, the ninja maintains some capability of maintaining meaningful uptime if disengaging from the boss for a few gcds. Mantra has been mostly rendered a moot point, though it still has use. The melee's current design (not tuning) would lead one to assume the following hierarchy.
Ranking
1. Samurai
2. Monk, Dragoon
3. Ninja
With that in mind, Black Mage would slot in at 2x or 3 spot - They have a fair amount of tools to deal with forced movement and mainly suffer in heavily extended periods, but they aren't too dissimilar from Red Mages in that regard. The current patch makes VerScathe less awful but likely still undesirable. Summoners maintain the most on demand mobility, though improper play leverages a tax for each step.
And the problem comes back again to Raise, as without them, Red Mage and Summoner are perfectly fine on the same rung of 2 / 3. The value Raise has fluctuates, but the end result comes back to consideration 1: The jobs who bring extras cannot deal equal or greater damage.
1. Samurai
2. Monk, Dragoon, Ninja
2/3. Ninja, Black Mage
4. Red Mage, Summoner
Ranged plain and simple have to come in last in their current iteration. The gap is what's debatable. This comes into consideration 3: A job's given strength should be assumed over a variety of encounters, not just ones tailored for it. A tailored encounter should be its chance to excel, not its chance to be passable.
What encounter 'tailors' to the Ranged? Effectively any encounter that doesn't tailor to Melee or Casters. Machinist has nothing that the other ranged do not, and therefore it is relatively easy to place this. The Machinist should do less damage than a Black mage, but more damage than any equally mobile jobs who bring extras.
Our final ranking looks like this.
1. Samurai
2. Monk, Dragoon, Ninja
2/3. Black Mage
4. Red Mage, Machinist
5. Summoner, Bard, Dancer
Now that brings consideration 2 into play. Why not just bring 4 melee if you can? While in an ideal world, encounter design would A) Potentially allow this at times but also B) It's still way better to bring a variety of jobs, for the sake of our concerns, it effectively means that the Highest performing of one role and the lowest performing of another role do not differ by more than about .96-1% of a raid's total damage at equal skill levels.
This means if your team clocks in at 90,000, the Samurai is not higher than 900 over a Summoner, or Bard/Dancer. Using some arbitrary numbers...
1. Samurai - 16,000
2. Monk, Dragoon, Ninja
2/3. Ninja, Black Mage
4. Red Mage, Machinist
5. Summoner, Bard, Dancer - 15,100
Ok I lied, we weren't almost done back there.
Now I doubt that's a universally accepted list (I often jest on the ones that do show up), but it's worth noting that this is assuming jobs in their tailored encounters.
The Samurai / melee fluctuate down as melee uptime is denied. The casters fluctuate down as more movement is demanded.