In Alexander Savage, the problem is two fold:
- There is nothing, lore wise, to look forward to as we already know what's going on because we saw it in Normal mode.
- The normal mode's story itself is so much cheese. No body cares about some goblins that want to conquer the world for all the cheese are belongs to them. Not only that, the things we end up fighting are just. Goblin machines.
Let's look at Coil:
Coil had the whole cataclysm (that changed the entire game's environments and world) behind it.
We had a good reason to go into the coils in the first place, with Alisaie seeking truth instead of cheesy Illuminati conspiracy to take... cheese.
We got to know about ancient Allag and its technology, reasons behind Dalamud/Coils. We fought things from monsters that took nesting to giant defense mechanisms, dragons, resurrected baddies and 2 super awesome primals in what I still consider the most epic encounters in FF history!

Originally Posted by
Bacent
So you want to further increase the gap between 'serious raiders' and people who are trying to get into raids/casual players? At the very least when they have normal versions first, it gives everyone, not just the special ones who clear stuff super quickly, a chance to gear up and possibly get into a new raid group.
Hell I have two classes geared up above i200, and people won't give me a damn chance to even learn stuff because I have no EXP in some stuff. I'd rather them keep it the way it is so more people at the very least have a 'chance' to try to get into something earlier on.
Whatever gear you get from normal Alexander is 10 item levels behind currency (a.k.a. welfare) gear and is also time gated. You will either do what raiders do and try to optimize by getting the cheap/fast to obtain pieces for your main to compliment what you can get with currency. Or you'll get pieces for alts. So said "gap" doesn't matter gear-wise.
Also, I hate to break it to you, but you having over whatever many i200 classes is irrelevant if you do not back that gear with research for optimal rotations, play-mindset and decent parses.
Speaking from personal experience here, I was uninterested in raiding for a long time due to uncertainties around me in real life. My character changed mains (and owners over my brother) from a tank to summoner (Though it did not matter at that point since I did not raid). But when I decided to rejoin the raiding scene, being so behind on item levels (ilv184), I managed to get into an A3S progressing group. Bear in mind, that being so well into the 3.07 patch, there was enough time to have a full ilv190 set from Alex Normal, and you would be closer to ilv200 with eso pieces. I got my first A1 and 2 Savage clears in that 1 go. Doing slightly sub-par but acceptable DPS. After all, I had not much practice, just knowledge of what needs be done.
Point being, it wasn't my ilvs, which were about 10 levels beneath any non-raider that kept up to date, that got me into raiding groups. It was my performance. If this applied to me, it should apply to anyone. And if a raid group "only" judges you based on your item levels, you do not want to join that group. Take it from me. 
So please, do not shoot off a suggestion that tries to bring back a huge portion of the fun in raiding in FFXIV due to some made-up excuses about "gaps" that don't matter/exist.