I like the idea of having a way to continue improving a piece of gear I have outside of just "Hey I got this better item, now to switch it out." I loved that I could continue to improve my relic in ARR without having to hope for a drop from other content. Now that I can do that with gear I'm all for it. It takes some RNG out of the improvement process. Something you can slowly work toward knowing you will get it - not running and running and running and not ever getting an upgrade because RNGod hates the color of underwear your decided to wear that day two months ago.
I like some RNG, but I also like being given an option to improve my gear that has no RNG (and that isn't just "Hey I bought a new shirt. Time to trade it for seals/stuff it in the retainer in case I want to glamour it later".) As far as I'm aware, you won't be able to overmeld the battle gear, so that RNG is a non-factor.
A grind is only a detriment to enjoyment if you are focusing soley on the fact that you are grinding/you are only doing the grind.
For example, I didn't/don't see any of the crystal farming in FATES for the new relic quest to be a grind/detriment to my enjoyment because I can do it on any class I want. I am therefore using this golden opportunity to level up other jobs that have been gathering dust at <60. Other players aren't doing that, soley doing it on the one job at 60 so it seems like a grind to them.
The "unidentified" grind I don't see as a grind either, because I'm doing bits and pieces all over the place (roulettes of old content which I'm so glad I get to run again with a bonus of being able to use the stuff I get out of it, finally repping up the beast tribe quests that I've been wanting to do but the mount just wasn't enough incentive, leveling other crafters to help my FC mates.) I'm literally just playing the game and getting progression toward my relic stages.
I find the problem most people have is that they tunnel vision into "NEED THIS DONE ASAP, TO DO THAT I NEED TO GRIND OUT ALEX XXX/DO XXX BEAST TRIBE/XXX HUNTS" and it is that mindset that is a detriment to the enjoyment of a game.
So there is my answer to how this "grind" improves my personal experience of the game, and from my standpoint, it's a huge improvement.