Yes, obviously. Which creates exponentially more work because --when it's not just a mere +X% damage by which to shuffle numbers on a meter and then unshuffle them back in a resultant log-- it's exponentially more gameplay available to each job in party play. The question is merely whether it's worth it, whether we actually want team play, or mostly just simultaneous play.
Honestly, most would be dependent upon actual undermechanical depth, such as not all elements doing the exact same thing (solely raw damage), let alone the same thing as physical damage. Those synergies are things that come pretty quickly and naturally out of fire having some appended mechanic, of wind having an appended mechanic, of multi-strike attacks actually having a intuitive difference from big, single-hit attacks, of attacks that seem--in their animations--to knock enemies to the ground or into the air, of mobs that have more ways to manipulate their behavior than just to be at the top a damage-times-modifier list (a.k.a. Enmity), etc.
Flare goes off in the middle of the enemy pack and for that brief moment, the Ninja has n-1 shadows to jump to. The White Mage draws a torrent from the lifestream (literally just taking advantage of ground on which heal or Holy casts previous landed) or draws up an occluding boulder (ala Stoneshield / ground-targeted Stoneskin) and the Ninja can use that block line of sight between enemies and himself and go into Stealth. The White Mage can project Fluid Aura through Suiton, adding that much potency-to-HP to its wave as it heals and cleanses allies, damages and purges enemies. Etc. Etc.
It's just a matter of having more to our abilities than mere timers, resource gauges, and linear unlock sequences so that a battle doesn't almost precisely as it did, save for perhaps holding an extra GCD before deploying oGCDs in one's opener, in party play as it does against a striking dummy. The synergies form simply from the types and classifications that'd come into play. That's not to say they wouldn't need a fair bit of balance so that, say, a Black&White NIN/BLM, DRK, WHM, PLD doesn't become the go-to speedrunning group for hard dungeons or the like or that you don't end up just stacking Monks and Warriors for the stagger they might induce on adds in a given Savage raid such that you don't even need a second healer. Such wouldn't be "easy". But it's not a fatally flawed course of action to have synergies, nor absurd to want more from party play. It's just more work... mostly because there's then more gameplay actually there.