IMHO SE only really have themselves to blame for the current disparity in skill level between progression raiders and the casual majority. Personally I can think of 3 ways in which SE could chose to address it.
1) Probably the most likely way forward would be to simply educate the masses better, the class quests and progression pretty much just throw new abilities at you and leave you to figure out what to do with it. In some cases it's fairly obvious and straightforward what you should be doing, but in many others, it's just like 'hey I got a new button, what do I do with it? It's quite clear that a good portion of the player base needs a nudge in the right direction for certain jobs.
2) The next approach is to simply force the player base to get good by the way of harder content. Now we all remember the drama over stuff like Steps, Ozma and Thordan EX, but I'm firmly of mind that people objected to these because they were sudden spikes of difficulty in a game that outside of coil progression and savage, was generally very easy going and forgiving. Having content gradually ramp up as you hit the end game would help alleviate these issues somewhat as well as raising the overall bar of player performance as people hit the actual end game.
3) This leads onto my third approach which is possible in some regards, and sadly unlikely in others. Yep you guessed it, SE would do well to make a players performance clearer and easier to digest. The manner in which dot damage is displayed to the player could use a rethink and of course, there are plenty of ways to clarify a players damage simply by taking data that's already there in the chat window and simply displaying it better.
Naturally I couldn't touch this topic without addressing parsing, and of course I agree that a fully featured recount style in game parser wouldn't go down well. Personally I feel that the harassment angle is significantly overplayed though, the tools to wave unwanted data in peoples faces have been in place for years now, this would really just even the playing field between PC and console players, as long as it was made clear that harassing a player over damage numbers regardless of it's source is still a reportable offence, things would be fine in my eyes.
However, there is a different approach I think SE could take with this, one that would be discrete, private and too vague to use as ammunition, but still be able to let the player know how they are performing in the grand scheme of things:
Simply put, the parameters bar (aka your HP/MP/TP bars) has an icon to the left of it that is useless. In my eyes it'd be fairly easy for SE to have an algorithm that worked out each jobs optimal single target DPS for a given iLvl, I would then take that number and break it down into sensible tiers and have the parameters bar icon display as such. For example, sub 40% of optimal DPS and you get a black icon, from 40%-60% you get bronze, 60%-80% gets you silver and 80%+ nets you gold. Aoe doesn't really need to be accurately displayed accurately really as aoeing is going to pad even a low tier player upwards which will give them the indication they are onto a good thing, this doesn't need to go into fine detail, it's purely there to show a player if they are on the right track or not.
A perhaps controversial way of taking this further would be to add achievements for hitting the various dps tiers vs end game content. Players who don't want to be called out on this stuff will typically have their achievements hidden as it's the default setting anyhow, but for those that are interested in their personal performance, it gives them something shiny to aim for and take pride in earning.
There is a 4th option of course, and that is for SE to simply let things continue as they are, but in my eyes, allowing such a disparity in playerskill to run unchecked is everybit as problematic as diving down the parsing rabbit hole. Whilst it's not really a problem in this tier, I stand firm in my belief that A4S would be nigh impossible for the overwhelming majority without either a parser within the group or optimal rotations and strategies based on data that required a parser to obtain in the first place.