The only ones I see even close to dying are both Last Wish and Garden, not including the teams that still run for 1K and Div. Aside from that, the loot just doesn't hold up in any way compared to what we have now.
Deep Stone and VoG also have exotics that people are chasing, but also has very good loot that is worth it in current endgame right now, so I personally don't feel like these raids are even close to dying.
I would say that Vow is far from dying as it's still a more recent raid and plenty of loot to go after, especially everyone that's going for their red border weapons.
Both of the loot from Garden and Last wish was bad back when they were the current raids.
This listing is more about full runs rather then specific encounter farming.
I have seen alot less activity for Vow of the deciple, i could only get a run in 2 weeks and even before that i have seen alot less lfgs for it.
LW weapons saw plenty of use, but they launched with an expansion that introduced about 80 new weapons, most of which equally powerful.
Apex Predator was great when Cluster Bomb was meta, otherwise is a mid rocket.
Supremacy was rivaled by Long Shadow, and later Persuader, but has always been good (even while lacking damage perks).
Techeun Force is an adaptive and couldn't compete with High-Impacts like Erentil or precisions like Main Ingredient.
Tyrrany of Heaven is still a solid option as far as bows go. Though it could use better perk selection
Nation of Beasts was, and still can be a solid energy HC, though better options exist now.
Age Old Bond is unfortunately a victim of being a 360 AR. It can't be saved
As for GoS weapons, they hold up now just as well as then, but desperately need updated perk pools. Most perk combos are strong and desirable, but aren't unique.
Ancient Gospel and Sacred Provenance are and were solid options, even with the old and limited perks that they have. They could use a light touch up, but just adding a few more relevant perks would help.
Accrued Redemption pretty much the same as Tyrrany
Reckless Oracle is pretty good for a 720. Rapid-Fire Autos could use a slight PvE buff, and a very slight Recoil change to make them more vertical, otherwise is a great and very unique Auto.
Omniscient Eye was held back by the fact that it is a Rapid-Fire, and it has bad perks for a Sniper. Even with powerful perks or perk combos, I don't see people using it now unless 140 Snipers are buffed or changed to actually matter.
Prophet of Doom is a precision SG, don't really know what to say about it. Not great in PvE, not used in PvP. Though I guess being one of 3 shotguns with One-Two punch made it a little more relevant then.
Zealot's Reward is pretty much the same as Omniscient. Without any stand-out perk it won't surpass Cartesian/Null
In any case, LW weapons aren't used much anymore due to much better options existing, and GoS weapons were used rarely (probably due to no one understand or enjoying the raid), but can/could easily be replaced or compensated for.
GoS also launched within the Pinnacle era, making most weapons at that time functionality irrelevant anyway