The lack of levels isn't the problem with the idea. It worked fine for Velious. Your proposed implementation just doesn't sound fun.
Unfortunately, it's the one that is in line with the current Modern WoW design trajectory. The one that gave us "level squish". And they will not make the suggested leap, because "locking" content behind specific bars (quest lines) is something they're against these days. The only bar to content should be time, and not too much of it.
There is a reason levels feel (felt?) good, and that's because they gave us a sense of progression. And no, the ding wasn't a sense of progression, it was a pavlovian reflex that associated ding with the real leveling: going to the trainer to purchase a new ability (even if it is Flash Heal XXI), opening the talent tree to add a new talent. Those actions were "tactile" rewards, rather than an invisible +1 STA, +1 INT. And they made the reward loop work.
Oh, and I forgot that suddenly, you were seeing +1 Sword Skill messages again. That was deferred reward, less tactile, but still working.
But Blizzard painted themselves in a corner by removing those tactile rewards, then rating increases guaranteed to drop your effective stats, THEN introducing scaling so that even the few +stats didn't even matter. At this point, each level gives you a negative feedback, except the last of the expansion which unlocks the game.
So, in that context, removing every level in the "leveling" makes sense. The only level that rewards you is the last one. And that is doomed to fail, because unless you make it so that you can complete that level (or that quest line) in a few hours, then it feels to remote, and you don't feel like you're progressing with any session.
There's no solution that doesn't involve a 180 in design. Which is not going to happen in WoW 1. And that's also why Classic holds so much lure...