So.. I think you kind of hit on why some tanks are so unpopular in your post.. unfortunately I also believe you focused too much on things that wouldn't ultimately matter. In the grand scheme of things, the amount of avid fans (those being people who have played every FF game, know the lore/skill sets for them, and love almost all things Final Fantasy) are going to be fairly slim compared to the run of the mill Final Fantasy games (fan of the playstyle, but don't really know all the lore, may have a favorite character, but probably can't name all of the skills) combined with the average MMO player who may not have a vested enough interest in Final Fantasy to even be considered a fan.
I also think you superimposed the tank role onto previous Final Fantasy games. I never considered Cloud a tank while running through FF7, nor do I consider Lightning a tank when going through 13. I actually don't really consider any of the characters a tank. Maybe that's just me, but playing something iconic doesn't factor into the role I am choosing to play.
The real brunt of the issue is the stress level. As has been mentioned before, tank roles (and healers) are stressful. Any mistakes you make are apparent, that goes for any MMO, not just this one. This one does take it a bit further in that tanking here is more difficult than tanking in other MMOs. It takes more concentration here and is less of a spam any of the hate building abilities. You can do abilities out of order in other MMOs and still hold threat, not as well, but it's still possible. Try that here and people are pulling off you in no time. Add to that the folks that want to rush through everything because that's how every other mainstream MMO works and you have a lot of frustrated people being scolded by their party.
The low damage also doesn't help, but that's not really going away. Even with increased damage of other MMOs, on boss fights tanks are still bottom by a fairly wide margin. I will give that a dps getting killed in a 10 man party in another game isn't always a big deal though, compared to losing a dps in an 8 man fight here (primals/coil). A DPS dying for most dungeons, however, can happen. Prior to 2.1 I've even had a dps afk for an entire dungeon and still ran it just fine. The only real dps check I can think of that will cause a wipe is Demon Wall, and even that you can skate by (it'll be close) if your healer is helping out.
I don't like some of the skill changes you suggested. I think Cover would be too over powered if it functioned as you described. I like Provoke as it is now for the most part (though I do wish they'd add a "attack you for 3 seconds" to it) because it requires dps to pay attention and stop attacking if they don't want to get hit. Having a stun that has no cooldown to it, and is off the GCD timer just screams overpowered to me as well.
I'll agree with effects applying prior to the animation, and that combat feels slow.. I disagree that removing the global cooldown will make it feel faster. Yes, you can use the skills faster, but in the end it's still the same 3-4 button rotation for most pulls.
In the end, I blame the community for shortage of tanks. Yeah, there are some tanks that are jerks... probably a lot of the ones that still play the class are the ones that don't give a rats behind what you have to say about them and will tell you so. That doesn't really leave a polite lot. The nicer ones probably got weeded out as they were trying to learn to play by people trying to speed through things, who insisted on pulling first, complained about loss of aggro, and started throwing insults around at the first mistake. Until the job is less stressful, and more forgiving to play, it is always going to be in a minority regardless of skill names/nostalgia or damage done. The same goes for the healer class.