In my personal opinion this option was meant for those who do not have a static raid group. Anyone with a static raiding group can get the Item Level 100/110, and 115 weapons with enough effort and practice put in. In fact it's probably the better option for the more casual types. You log in, raid for about 1 to 2 hours, and you're done.
However the Quest Weapons (Relic, Novus, Nexus, whatever) will take considerably more grinding time. RNG is involved, many dungeon runs, lots of spiritbinding involved. It basically becomes a full time job from when you log on, until you log off. Not my personal idea of fun, but I know some people who have enjoyed it. Is it worth it? That's based on the players opinion.
While I agree the last weapon in the quest series can be the best in slot item for your class, I personally don't feel like spending the time, effort, or money on it. I have my ilvl 115 Weapon already from 2nd Coil, and while the stats aren't what I would prefer, 30+ extra determination isn't going to make or break my ability to heal through current content. If anything, I tackled most of the content without the Quest Weapons, I think the only time I used them was during the 1st Coil, and trying to get them upgraded through the various objectives it had me doing.
Right now the most fun I have in the game is raiding. Everything else to is me a mindless grind. Keep in mind though this is just my opinion. I don't feel they should change the current quest line for these weapons only due to the fact it's completely optional, and not at all required for anything in the game other then a status piece of equipment. That and some of them do look pretty awesome won't lie. You don't need these weapons for Dungeons, Trials, or even Raiding. This has been proven by just about everyone out there completing 2nd Coil.
Will the weapons help? Sure of course they will, but actually completing the quest is up to the player, and for them to decide if it's worth it. Me personally, no it's not worth it, which is why I'm casually doing the quest. I have yet to start inserting Materia on the scroll for whichever part of the weapon quest I'm on. I refuse to pay absurd amounts of money for it on the market boards, and spiritbinding is so mind-numbingly boring to me, I'd rather be doing something else. I may eventually get the weapon, but it's by far not in my top 10 priority list.
Just my 2 cents, take it with a grain of salt.