Really i think what Blizzard needs to do is reuse the covenant framework, trim it down, and then tie it more to the reputation.
You don't get any player power that is useable in raids or other instanced content, but you do get a storyline, zone upgrades, and a few unique cosmetics.
Then, instead of choosing one covenant or rep and sticking with it, you instead have all of them available, but limit how much progress you can do with them.
You can still opt for one reputation and go fast with that one, but that would mean everything else going slower, or you can try and spread it out, but being slower overall.
This way you have most of the upsides of covenants, but tied more to reps instead of being a weird not-quite rep. If you like one zone more than others you can still focus on that one and get full rewards. Or if you want everything you can try and spread it out and still get everything.