Alexander: Coil worked more than fine and, while I understand that you listened to some players, you should have noted that they weren't the majority of the playerbase. You always talk about looking at the statistics and all that, didn't you see what happened with Savage Coil? Why did you design Alexander like that then? As has been said countless times, all that was needed was the "story" version with lesser rewards (or none at all, people were fine with it when it was discussed in the forums) while keeping in the main raid the same difficulty than the previous raid series. You could even release them at once that way, and we would do whatever we like instead of having people farm the "same" raid twice and getting bored (more on that later).
Diadem: At this point I thought that you would already know what happens with that kind of content (FATEs, hunts, etc.). Let's see what you're going to change.
Anima weapon: Well, this is related to the other two points too. First, and most important, we pay (or paid) you because we wanted to log in and have fun, so if something feels like a chore you should go back to the drawing board and think about something better.
Second, right when ARR launched we didn't have these ilvl issues at all. We're back to what has happened with Savage. Just because some people complained about "John has the same ilvl than me" you broke the whole game, and now you have all these problems (the primary motivation should be having fun, not the carrot in the stick, so forcing people into something that they don't enjoy WON'T work, as seen with Savage). Moreover, if you focused a bit less about "ILVL ILVL ILVL", forgot about this insane vertical progression and moved to a diagonal progression instead, it would fix a whole lot of these issues. Players would feel that their efforts matter for more than a couple of months, their effort would be more worth it in their eyes, there would relly be a real sense of progression, and you would also keep content relevant for more time (multiple paths to get equivalent -not the same- gear) without trying to keep it artificially by "forcing" us to farm it 99999999 times.
And finally, and as Alexander_Dragonfang has explained more than fine, that whole time = reward is a very VERY bad idea. As I've said, the focus should be "having fun", be it by having a challenge or by playing something else that you enjoy. Doing again for another whole lot of times content that you have already done a million times before, or relying on insane RNG or gil sinks for a reward that will last one month, is not fun, it's a chore and it burns people. I don't really know what's wrong with how the relic worked in 2.0, or even in FFXI, as getting it wasn't as hard as completing Coil and, as it's difficulty was in the middle, it also prepared people to get into the harder raid. We had the choice there, and the way it worked it made people get a true sense of achievement once they got their relic and even encouraged some of them to try Coil, the "next" step (and also were we used said weapon). Also, what we did was content that was fresh, as we were doing it for the first time while doing the relic quest and, even if we wiped countless times in Titan, we didn't feel the same amount of burnout that we feel(t) with later relic questlines.
TL;DR: As you said some time ago, fun comes first. If something isn't fun you're doing it wrong, and it doesn't matter why you're doing it.