More interesting loot please! Here are some ideas!

[kyuven]

Uh huh... you never played FFXI did you? Most of the higher level gear had unique effects, and we rarely ever had problems with one person needing a specific equip. The reason why is pretty simple, it's because there was plenty of other OPTIONS available which were just as good.

And do you remember how people would devise macros for switching gear mid-battle, going so far as to switch gear between attacks?
FFXI had a lot of "interesting" stats but it eventually ran into the same problems as EQ, compounded with numerous other issues.
There's a really good reason we can't switch equipment in combat.
In addition, inventory space in this game is limited as it is. Starting with this expansion, there will be precise one fewer jobs/classes than there are Armoury inventory slots. Having more "options" for gear, even in cases when it's not necessary.
In addition, many stats from FFXI simply aren't necessary in FFXIV:
Let's take your examples:
Gear which enhanced particular weapon skills: We don't have weapon skills. Even WoW got rid of these.
Gear which enhanced cure potency: Determination does that already.
Gear which could give you an advantage over a certain type of monster: Maybe, but do you really want to haul around 40 different items for each type of monster? Also, bosses in the game wouldn't be typed anyway to prevent exploiting this.
Gear which could refresh your mana: Again, superfluous since mana/TP regeneration is closely managed. FFXI was much slower paced and could get away with this, XIV is faster paced and thus we actually regenerate it faster in combat than XI did while out of combat. This is before getting into how certain classes have their own means of mana generation that having regen items would mess with. A BLM, for example, would basically be REQUIRED to get these items.
Gear which could regen your health: Again, useless since we regenerate health so quickly on our own, and unless it's a LOT of HP per tick, it's not going to make a difference. And since many boss fights rely on mechanics that involve DoTs, this would have item-select forcing akin to the BLM example.

Basically, FFXI's gear with unique effects was a means to let characters become stronger, since there were certain things in the game that NEEDED to become stronger, but none of the stats covered it. I'd even argue that many of these were superfluous within the game itself.

This whole assumption that you'll need X piece of gear to do content is completely unfounded and I can't think of any situation in any MMO I've played that it's actually happened. It's an attitude like this, one grounded in inexperienced assumptions, that's going to keep this game bland.

In EQ1 there were at least two major examples:
1) "Clicky" items. If you didn't have an item (and i mean it, "an item." You had a lot of choices in this regard. All of them expensive.) you could right-click to gain a temporary buff, you were useless in a raid. This was because the developers had a hard-on for giving bosses AOE dispels, and losing your buffs meant losing the fight. Having "junk buffs" was a way to mitigate this. No clicky, no raid.
2) The cleric epic weapon. Many epic weapons (the equivalent of XI and XIV's relic and zodiac weapons) ranged in usefulness from "pretty nice" to "only useful for the stats." The cleric epic, however, was a completely different animal: It gave a mana-free 96% exp restoring resurrection when right clicked. In a game where you could lose a day's worth of exp in a single death, it was incredibly useful. Being able to use it in combat (since EQ didn't have a distinction between "in combat" and "out of combat" at the time) made it indispensable. As in literally. You weren't considered a "real" cleric without it. And considering only one of these could enter the game per week, it was pretty rough being a cleric back then. It got so bad that when they added "AA points" (think XI's capacity points) one of the first ones they added was an insta-cast rez spell. The cleric epic was STILL better since it didn't have a recast time.