While i can certainly agree with wanting Crafters to interact more with Raiders, but forcing those who enjoy raiding to have their raid gear crafted by some random guy, who may not even get it HQ after you went to the all the trouble of downing the encounter sounds like a terrible idea.

What i think should happen is that Raids, such as Coil and the Primals, drop materials themed to those Raids in addition to what they drop regularly. These materials can be used to create alternate, same item level gear with similar stats. Maybe even in some cases the crafted stuff is just exactly what the boss would ordinarily drop,
This would help take the sting out of RNG never ever dropping gear for that one guy who has no luck whatsoever and is forever behind the gear curve in your static as a result.

They could even have specialty sets from the Primals that are themed to the presentation of the Primal itself, Like Ifrit and Titan themed Armor.

Such a system would include the ability to have a Crafter make something with Materials in your Inventory, much like the way the Materia Meld Requests work. That would allow the Materials obtained to be non-tradeable while keeping the ability for Crafters to join in.
The Item would be automatically deposited in the Material owners Inventory so it doesn't just become another Market Board vanity thing.

Such an idea would allow crafters to be in some form of demand by Raiders outside of niche 1% cutting edge crews. Who most likely craft their own gear.