Axes & Tridents with "impossible" enchantments are now in the game, as survival loots, in the way that you can't farm it at all.

Rare Trident have Looting II or III and Sharpness III IV or V.

Rare Diamond Axe have Looting III.

igloo_chest has 100% chance to hold a Rare Trident.
buried_treasure has 25% chance to hold a Rare Diamond_axe.
underwater_ruin_big has 50% chance to hold a Rare Trident.
underwater_ruin_small has 10% chance to hold a Rare Trident.
pillager_outpost has 25% chance to hold a Rare Diamond_axe.


v8 for 1.20.5
v6 v7 for 1.20, 1.19, 1.18 (maybe it works with 1.17 and previous versions)
v1 to v5 Working on Minecraft 1.14, 1.15, 1.16, 1.17.


Working in multiplayer.

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Rare-Trident-Axe-1.20.5-v8 - What's new?

• Buried_treasure has now 25% chance to hold a Rare Axe. (was 10%)
• Pillager_outpost has now 25% chance to hold a Rare Axe. (was 10%)
• igloo_chest always get a Rare Trident. (was 50%)
• underwater_ruin_big has 50% chance to hold a Rare Trident. (was 20%)
• underwater_ruin_small has 10% chance to hold a Rare Trident. (was 5%)
• End_city_treasure removed rom datapack.
• Datapack version 41.
• pack icon changed.
  
  Rare Diamond_Axe is now always Looting III, plus get random enchantments (level 30).
  Rare Trident is now always Looting II or III and Sharpness III IV or V, plus get random enchantments (level 30).

Rare-Trident-Axe-1.20-v7 - What's new?

• No change for players: 1.20 loot-tables changed, Rare Trident Axe adapted. (1.20 added Armor trim to some chests)
• added a notification message on datapack loading.

Rare-Trident-Axe-1.18-v6 - What's new?

• No change for players: 1.18 loot-tables changed, Rare Trident Axe adapted.

Rare-Trident-Axe-1.16-v5 - What's new?

• Elder Guardian no longer drop Rare Trident. (neither his head)
• Buried_treasure has now 10% chance to hold a Rare Axe. (was 5%)
• Underwater_ruin_big has now 20% chance to hold a Rare Trident. (was 10%)
• Added: underwater_ruin_small has now 5% chance to hold a Rare Trident.
• Added: pillager_outpost has now 10% chance to hold a Rare Axe.

Rare-Trident-Axe-v4 - What's new?

• Rare Trident is now Sharpness or Looting. (Removed Fortune and Power; Power doesn't trigger on Trident)
• Guardian no longer drop Rare Trident.
• underwater_ruin_big has 10% chance to hold a rare Trident.
• Elder_guardian can now drop his head.
  > 20% chance without Looting.
  > 80% chance with Looting III.

Rare-Trident-Axe-1.14-v3 - What's new?

• Guardians had 0.1% chance to drop a rare Trident without looting, and 30.1% with Looting III !!!!
  Now, a mistake is fixed : 0.1% without looting, and 0.4% with Looting III.

Rare-Trident-Axe-1.14-v2 - What's new?

• Chances to get a rare Trident on an Elder guardian was too low. Now it's quite good chances. (40% without looting)
• Added a 0.1% chance to drop a rare Trident on a guardian.
• Added a 10% chance to get a rare Trident in a buried treasure.
  

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Some things to know:

Power V is NOT used by Tridents when thrown.

Instead, Sharpness add damage to the Trident, in melee and in thrown status!

You can't merge Looting and Sharpness Enchantments on a trident: means that getting a Sharpness V or a Looting III is even more rare!


My original wish was to unlock Sharpness on tridents, and Impaling on swords, being mutual excluding (Sharpness or Impaling or Smite...etc), and also unlock Looting III on Trident and Axe. But datapacks are still limited.

And adding Fortune III to Tridents because it seems perfect for plowing the land. But in gameplay it would be totally useless.