I'm sorry, but you're thinking of hunts, not raids.
I've run so many 24 man raids that I've earned over half of my weekly poetics doing them and I can safely say that you're either the unluckiest person ever when it comes to queuing or you're exaggerating like crazy.
And you want leisurely grinds? Go fishing. There's no reason for the relic weapon quest to be as boring AND devoid of storyline as it is. You don't seem to understand the fact that something can be both time-consuming AND fun, and not "masochist who enjoys boredom fun" but REAL fun.
I'm surprised there are no pet grinds in FFXIV: many of the mobs in WoW have a .01% chance of dropping a pet, the DEFINITION of boring grind, but it's there for people like you.
