There is nothing wrong with class synergy, and I would even say that there is nothing wrong with meta (even perhaps that it's unavoidable), it ONLY becomes an issue when the discrepancy is so great that it cannot be reconciled (See also: physical meta/RIP casters, the tyranny of trick attack, requirement of DRG for BRD+MCH).
One way to "fix" this issue is to do as you said and remove synergy, but that makes for boring gameplay. In my opinion, what should be done instead is more regularly spread buffs so they aren't so exclusive:
-Disembowel is a perfect example: there is NO reason that after all this time BRD/MCH should not be able to apply their own piercing down, in fact it's ridiculous that they can't.
-Buffs like Brotherhood and Embolden should also affect (and be affected by) magic damage, this would help upheave the physical meta.
-Double DPS roles should be "punished" in some small way where it pertains to BRD+MCH. Perhaps Hypercharge and Battle Voice cannot be used concurrently somehow, or some other efficiency loss. This would leave the proper comp to be one "main" melee (SAM or MNK) one "auxiliary" melee (DRG or NIN) one ranged and one caster for 8 man content.
-On the same note as the above bullet, ALL jobs should have SOME kind of raid-wide utility buff including SAM and BLM, even if it's just one three minute cooldown like Battle Litany. This would mean that there is no PURELY "selfish" DPS job even if it's a small gain or "less than" from NIN or BRD. Pure damage classes will always get shunned where party play is concerned because parties want TO BE FED, parties don't want TO FEED ONE PLAYER. At least that way it's SOMETHING that can be brought to the table. Perhaps BLM could get a party wide speed buff that cancels Ley Lines and extrapolates it out to the whole party on 180s recast and SAM could get some kind of speed buff as well. I'd also propose perhaps Enochian giving +2% speed while it's up much like BRD gives +2% crit with songs while they're up.
-Radiant Shield and Contagion should be in the same pet slot and be consolidated into just damage up instead of separated into physical and magical damage
Feel free to help brainstorm more solutions like this.