Here are some options I came up with that I could potentially justify giving up a primary for... maybe.
Immovable Object - Can no longer be moved by enemy abilities. (Immune to knockback, vortex, wormhole, and do not run when feared). : nice defensive option
Rose Quartz - Double the effect of Life per Second, Life on Kill, and Health Globe Bonus : survivability that may be worth a primary stat
Second Wind - Gain max primary resource when attempting to use an ability with insufficient resources. (1 min cooldown) : resource management tool that may open up more builds
Wide Reach - Double the effects of Pick Up Radius : quality of life and potential for WDs
Maniacal Rage - Increase damage by 100% for 8 seconds after earning a massacre bonus. : much farming
Insatiable Greed - Decrease all cooldowns by 5 seconds after picking up 10,000 gold (from a single pile) : feel less bad about +gold affixes and potential for cooldown builds
Phoenix Coal - When receiving fatal damage, you are instead healed to 35% of maximum life and explode (15 yds) for 10x damage prevented (multiplied before mitigation calculations), 5 minute cooldown. : 10x may or may not be too much but may be nice for HC and potential for a fun effect
Steady Rock - Abilities that generate primary resource deal double damage. (must actually generate, i.e. doesn't work when at max) : may open up more builds
Fossilized Flower - Increase all damage by 20% when all 3 class specific item types are equipped (i.e. wand/orb/wiz hat). : more build options
Blessed Stone - When gaining a shrine effect, gain another random shrine effect. (shrines only, no pylons) : fun and potential to justify losing a primary stat
Dark Amphibole - Increase damage by 5% for 10 seconds when healed by a health globe at max health. (up to 10 stacks) : farming help and gives health globes some additional effect when otherwise useless
Flaking Stone - Rare items drop as Veiled Crystal and Magic items drop as Arcane Dust. : huge quality of life bonus
Magnifying Glass - 10% chance for gems to drop 1 tier higher. : quality of life and gold savings (not that the gold part is a big deal really)
Prismatic Sphere - All elemental damage bonuses are equal to your highest elemental damage bonus. : opens up a lot more builds and makes changing builds much less painful
Hearthstone - Halve the time required for Town Portal and increase movement speed in town by 100%. : quality of life, potential for HC survivability
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Immovable Object - Can no longer be moved by enemy abilities. (Immune to knockback, vortex, wormhole, and do not run when feared). : nice defensive option
Rose Quartz - Double the effect of Life per Second, Life on Kill, and Health Globe Bonus : survivability that may be worth a primary stat
Second Wind - Gain max primary resource when attempting to use an ability with insufficient resources. (1 min cooldown) : resource management tool that may open up more builds
Wide Reach - Double the effects of Pick Up Radius : quality of life and potential for WDs
Maniacal Rage - Increase damage by 100% for 8 seconds after earning a massacre bonus. : much farming
Insatiable Greed - Decrease all cooldowns by 5 seconds after picking up 10,000 gold (from a single pile) : feel less bad about +gold affixes and potential for cooldown builds
Phoenix Coal - When receiving fatal damage, you are instead healed to 35% of maximum life and explode (15 yds) for 10x damage prevented (multiplied before mitigation calculations), 5 minute cooldown. : 10x may or may not be too much but may be nice for HC and potential for a fun effect
Steady Rock - Abilities that generate primary resource deal double damage. (must actually generate, i.e. doesn't work when at max) : may open up more builds
Fossilized Flower - Increase all damage by 20% when all 3 class specific item types are equipped (i.e. wand/orb/wiz hat). : more build options
Blessed Stone - When gaining a shrine effect, gain another random shrine effect. (shrines only, no pylons) : fun and potential to justify losing a primary stat
Dark Amphibole - Increase damage by 5% for 10 seconds when healed by a health globe at max health. (up to 10 stacks) : farming help and gives health globes some additional effect when otherwise useless
Flaking Stone - Rare items drop as Veiled Crystal and Magic items drop as Arcane Dust. : huge quality of life bonus
Magnifying Glass - 10% chance for gems to drop 1 tier higher. : quality of life and gold savings (not that the gold part is a big deal really)
Prismatic Sphere - All elemental damage bonuses are equal to your highest elemental damage bonus. : opens up a lot more builds and makes changing builds much less painful
Hearthstone - Halve the time required for Town Portal and increase movement speed in town by 100%. : quality of life, potential for HC survivability