Well SE is already attempting to do the former in regards to forgetting about classes. The problem is I don't think they anticipated the 3 new jobs being as poorly received as they have been so they're scrambling to improve them. Unless they change how those work offering more cross class abilities for them won't do much good because they're already built to be a "hybrid" of the two other jobs that share their roles (or Machinist's case the...one other job x--x ).
And I think that attempt to hybridize them is what made this seem like all classes were losing their individuality. Before they came there wasn't really that much of a complaint as all of the classes/jobs actually played pretty differently from one another. And most of them haven't changed in that respect, I just think people are blowing those changes out of proportion. Again, except the three new jobs. They feel too samey. So it feels like we didn't get anything new gameplay wise. Which is why I think we're not really going to be able to get a handle on how to "fix" this issue until they figure out how to balance the new jobs while giving them a unique identity (aka make the mechanics behind them that were supposed to make them unique actually useful. That seems to be the biggest complaint on that front from what I've been reading).
But the idea of skill books in general sort of like recipe books for the crafters, that might potentially be possible since we already have a similar system. As much as I like cross class abilities I'm willing to admit it's clear they're trying to move away from the system. So rather than being "cross-class" abilities I guess it would be more semblance of an optional PvE skill set you could hunt for whatever lore reason. Like "Oh look! BLMs could heal after studying the CNJs'. We can do something similar with the dark powers of the void" or however you'd go about it.
Or like was suggested earlier in the thread: give people the ability to aesthetically change how their skills appear.
And thisI want the devs to get back into adding really unique jobs. Blue Mage in particular could have a lot of what people here are asking for.