Here's a list of weapons (most were widely used at some point) that have either not been reprised with relevant perk pools in years, have never existed with random rolls and have not been reprised, or are curated rolls (ritual weapons) and should be placed in activity loot pools with random rolls.
Vanguard:
• Oxygen SR3 | Scout Rifle
• Service Revolver | Hand Cannon
• The Last Dance | Sidearm
• Main Ingredient | Fusion Rifle
• Archimedes Truth / The Long Goodbye | Sniper Rifles
• Curtain Call | Rocket Launcher
• Edgewise | Machine Gun
Gambit:
• Gnawing Hunger | Auto Rifle
• Night Watch | Scout Rifle
• Pillager / Exit Strategy | Submachine Guns
• Lonesome | Sidearm
• Parcel of Stardust | Shotgun
• Doomsday | Heavy Grenade Launcher
• Bad Omens | Rocket Launcher
• 21% Delirium | Machine Gun
Crucible:
• Martyr's Make | Auto Rifle
• Does Not Compute | Scout Rifle
• Redrix's Broadsword | Pulse Rifle
• Hard Truths | Submachine Gun
• The Vow | Bow
• Critical Sass | Fusion Rifle
• Gentleman Vagabond / Revoker | Sniper Rifles
• Play of the Game | Heavy Grenade Launcher
• Komodo-4FR | Linear Fusion Rifle
Iron Banner:
• The Forward Path | Auto Rifle
• Frostmire's Hex | Scout Rifle
• The Time-Worn Spire | Pulse Rifle
• The Steady Hand | Hand Cannon
• The Fool's Remedy | Sidearm
• Felwinter's Lie | Shotgun
• Orewings Maul | Breach Grenade Launcher
• The Day's Fury | Heavy Grenade Launcher
Trials of Osiris:
• The Scholar | Scout Rifle
• Aisha's Embrace | Scout Rifle
• Forgiveness | Sidearm
• Exile's Curse | Fusion Rifle
• Burden of Guilt | Fusion Rifle
• Reed's Regret | Linear Fusion Rifle
Seasonal:
• Pluperfect | Auto Rifle
• Steelfeather Repeater | Auto Rifle
• Seventh Seraph VY-7 (SMG)
• Seventh Seraph SI-2 (Sidearm)
• Seventh Seraph CQC-12 (Shotgun)
• Gallant Charge | Fusion Rifle
• Trophy Hunter | Sniper Rifle
• Pyroclastic Flow | Rocket Launcher
• Temporal Clause | Machine Gun
• Seventh Seraph SAW (Machine Gun)