I generally disagree with that premise because the point of difficulty IMO is not to justify bigger rewards, but rather to keep people of different talents and engagement levels entertained, no more no less. And in single-player games, that is deemed perfectly acceptable and common practice since ages - it's just MMOs in which people think harder difficulties should naturally come with bigger rewards and I think the sole reason for that is the ability to flaunt.
Similarly, power/iLvL IMO is not a reward, but a means to an end - and we're sorely lacking in ends in the casual department. It "could" serve to adjust the raid difficulty naturally, so that a geared "casual" would be able to pug and beat the raid as he would now beat normal mode, but the mechanic heavy raid design doesn't support this, plus the power gained from items doesn't make enough of a difference until several patches (or expansions) later. There's no casual content that requires you to be geared either - all content that requires good gear also requires coordination beyond pugs. It's pretty much gearing up for gearing up sake and that _is_ an issue, because as you say, there are no real goals.
That aside, the way you outline the suggestion doesn't really draw a clear line, even if the quests were mutually exclusive, because progressing along the hardcore path automatically progresses along the casual one, as the progression metric (iLvL) is identical and the usage isn't mutually exclusive. It just progresses further. As such, it also doesn't help with your goal issue, it just cuts off your progression earlier until you switch to hardcore.
I agree, though, that extending the relic system to more gear and thus opening up another gearing method as such might be beneficial. Gearing as is isn't very diverse, both in acquisition (though tomes have innate content diversity) and the gear itself: I think there's not a single vit/crit/det choker for tanks over i190. I would expect at least every stat combination to be represented for every slot on each iLvL plateau >_>