I think a bigger issue with job-specific set bonuses like that some effects may be too powerful to be replaced by anything else, which can cause problems down the road. Imagine if the healers all required ilvl 90 gear even when doing ilvl 200 content just due to the invaluable ability bonuses? Or say a new player needs to hit up Labyrinth of the Ancients or other dead content for a vital piece but no other class needs to run that.

If ability specific bonuses are added, care would need to be taken to ensure they get replaced eventually like all gear, or the entire system FFXIV runs on would need to be entirely overhauled (which I really don't see happening).

That all said, back to the original topic, I would LOVE to see set bonuses on more gear... just most likely it'd need to be basic stats, or standardized (say, Healer gear gets a 10% healing potency bonus for 5 sets on all 8-man raid gear)